Laurence Carassus est directeur du DVRC et directeur de la recherche pour l’ESILV. Elle est professeur des universités à l’université de Reims. Diplômée à Dauphine d’un Master 2 en Mathématiques Appliquées, Laurence est également titulaire d’un Doctorat en Mathématiques Appliquées à Paris 1 Panthéon-Sorbonne, préparé au CREST, et d’une HDR (Habilitation à Diriger la Recherche) en Mathématiques Appliquées à Paris 7. Après avoir été monitrice à Paris 1 et ATER à Paris 9, elle obtient un poste de maître de conférences à Paris 7. Elle participe au Master 2 Modélisation Aléatoire puis monte le master Ingénierie Statistique et Informatique, de la Finance, de l'Assurance et du Risque. Laurence rejoint ensuite Deloitte Risk Services en tant que Manager et intervient sur des missions d’audit et de conseil dans les domaines de la banque et de l’énergie. De retour à Paris 7, elle obtient son HDR et est promue professeur des universités à Reims, où elle gère le master Statistique pour l’Evaluation et la Prévision. Pendant sa carrière, Laurence a enseigné des cours de finance, de probabilités et d’autres domaines des mathématiques, essentiellement en master à l’université mais aussi à l’ENSAE et dans le cadre de la formation continue. Laurence publie régulièrement pour des revues de 1er plan comme Mathematics of Operations Research, Mathematical Finance ou encore Annals of Applied Probability. Elle a participé à de nombreuses conférences et a été invitée dans des universités étrangères. Elle a également publié deux livres « Modèles de marchés financiers en temps discret: cours et exercices corrigés » avec G. Pagès, chez Vuibert et « Probabilités : cours, exercices et problèmes corrigés », chez De Boeck Sup.

## Articles de journaux |

Laurence Carassus; Jan Obł ́oj; Johannes Wiesel The robust superreplication problem: a dynamic approach Article de journal financial mathematics, 10 (4), p. 907 - 941, 2020. @article{Carassus2020b, title = {The robust superreplication problem: a dynamic approach}, author = {Laurence Carassus and Jan Obł ́oj and Johannes Wiesel}, url = { https://www.researchgate.net/publication/330034750}, year = {2020}, date = {2020-07-16}, journal = {financial mathematics}, volume = {10}, number = {4}, pages = {907 - 941}, abstract = {In the frictionless discrete time financial market of Bouchard et al.(2015) weconsider a trader who, due to regulatory requirements or internal risk manage-ment reasons, is required to hedge a claimξin a risk-conservative way relativeto a family of probability measuresP. We first describe the evolution ofπt(ξ)-the superhedging price at timetof the liabilityξat maturityT- via a dynamicprogramming principle and show thatπt(ξ)can be seen as a concave envelopeofπt+1(ξ)evaluated at today’s prices. Then we consider an optimal investmentproblem for the trader who is rolling over her robust superhedge and phrase thisas a robust maximisation problem, where the expected utility of inter-temporalconsumption is optimised subject to a robust superhedging constraint. This util-ity maximisation is carrried out under a new family of measuresPu, which nolonger have to capture regulatory or institutional risk views but rather repre-sent trader’s subjective views on market dynamics. Under suitable assumptionson the trader’s utility functions, we show that optimal investment and consump-tion strategies exist and further specify when, and in what sense, these may beunique.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In the frictionless discrete time financial market of Bouchard et al.(2015) weconsider a trader who, due to regulatory requirements or internal risk manage-ment reasons, is required to hedge a claimξin a risk-conservative way relativeto a family of probability measuresP. We first describe the evolution ofπt(ξ)-the superhedging price at timetof the liabilityξat maturityT- via a dynamicprogramming principle and show thatπt(ξ)can be seen as a concave envelopeofπt+1(ξ)evaluated at today’s prices. Then we consider an optimal investmentproblem for the trader who is rolling over her robust superhedge and phrase thisas a robust maximisation problem, where the expected utility of inter-temporalconsumption is optimised subject to a robust superhedging constraint. This util-ity maximisation is carrried out under a new family of measuresPu, which nolonger have to capture regulatory or institutional risk views but rather repre-sent trader’s subjective views on market dynamics. Under suitable assumptionson the trader’s utility functions, we show that optimal investment and consump-tion strategies exist and further specify when, and in what sense, these may beunique. |

Romain Blanchard; Laurence Carassus No-arbitrage with multiple-priors in discrete time Article de journal Stochastic Processes and their Applications, 2020. @article{Blanchard2020b, title = {No-arbitrage with multiple-priors in discrete time}, author = {Romain Blanchard and Laurence Carassus}, url = {https://doi.org/10.1016/j.spa.2020.06.006}, doi = { 10.1016/j.spa.2020.06.006}, year = {2020}, date = {2020-06-30}, journal = {Stochastic Processes and their Applications}, abstract = {In a discrete time and multiple-priors setting, we propose a new characterisation of the condition of quasi-sure no-arbitrage which has become a standard assumption. We show that it is equivalent to the existence of a subclass of priors having the same polar sets as the initial class and such that the uni-prior no-arbitrage holds true for all priors in this subset. This characterisation shows that it is indeed a well-chosen condition being equivalent to several previously used alternative notions of no-arbitrage and allowing the proof of important results in mathematical finance. We also revisit the geometric and quantitative no-arbitrage conditions and explicit two important examples where all these concepts are illustrated.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In a discrete time and multiple-priors setting, we propose a new characterisation of the condition of quasi-sure no-arbitrage which has become a standard assumption. We show that it is equivalent to the existence of a subclass of priors having the same polar sets as the initial class and such that the uni-prior no-arbitrage holds true for all priors in this subset. This characterisation shows that it is indeed a well-chosen condition being equivalent to several previously used alternative notions of no-arbitrage and allowing the proof of important results in mathematical finance. We also revisit the geometric and quantitative no-arbitrage conditions and explicit two important examples where all these concepts are illustrated. |

Laurence Carassus; Miklós Rásonyi Risk-Neutral Pricing for Arbitrage Pricing Theory Article de journal Journal of Optimization Theory and Application, 186 , p. 248 - 263, 2020. @article{Carassus2020, title = {Risk-Neutral Pricing for Arbitrage Pricing Theory}, author = {Laurence Carassus and Miklós Rásonyi}, url = {https://link.springer.com/article/10.1007/s10957-020-01699-6}, doi = {10.1007/s10957-020-01699-6 }, year = {2020}, date = {2020-06-23}, journal = {Journal of Optimization Theory and Application}, volume = {186}, pages = {248 - 263}, abstract = {We consider infinite-dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide a dual characterization of the superreplication cost. Then, we show the existence of optimal strategies for investors maximizing their expected utility and the convergence of their reservation prices to the super-replication cost as their risk-aversion tends to infinity.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We consider infinite-dimensional optimization problems motivated by the financial model called Arbitrage Pricing Theory. Using probabilistic and functional analytic tools, we provide a dual characterization of the superreplication cost. Then, we show the existence of optimal strategies for investors maximizing their expected utility and the convergence of their reservation prices to the super-replication cost as their risk-aversion tends to infinity. |

Romain Blanchard; Laurence Carassus Convergence of utility indifference prices to the superreplication price in a multiple-priors framework Article de journal Mathematical Finance, 2020. @article{Blanchard2020, title = {Convergence of utility indifference prices to the superreplication price in a multiple-priors framework}, author = {Romain Blanchard and Laurence Carassus }, url = {https://arxiv.org/pdf/1709.09465v1.pdf}, year = {2020}, date = {2020-03-17}, journal = {Mathematical Finance}, abstract = {This paper formulates an utility indifference pricing model for investors trading in a discrete time financial market under non-dominated model uncertainty. The investors preferences are described by strictly increasing concave random functions defined on the positive axis. We prove that under suitable conditions the multiple-priors utility indifference prices of a contingent claim converge to its multiple-priors superreplication price. We also revisit the notion of certainty equivalent for random utility functions and establish its relation with the absolute risk aversion. }, keywords = {}, pubstate = {published}, tppubtype = {article} } This paper formulates an utility indifference pricing model for investors trading in a discrete time financial market under non-dominated model uncertainty. The investors preferences are described by strictly increasing concave random functions defined on the positive axis. We prove that under suitable conditions the multiple-priors utility indifference prices of a contingent claim converge to its multiple-priors superreplication price. We also revisit the notion of certainty equivalent for random utility functions and establish its relation with the absolute risk aversion. |

Laurence Carassus; Miklos Rasonyi Risk-averse asymptotics for reservation prices Article de journal Annals of Finance, 7 (3), p. 375–387, 2018. @article{Carassus2018cb, title = {Risk-averse asymptotics for reservation prices}, author = {Laurence Carassus and Miklos Rasonyi}, editor = {Springer-Verlag …}, doi = {10.1007/s10436-010-0167-1}, year = {2018}, date = {2018-11-01}, journal = {Annals of Finance}, volume = {7}, number = {3}, pages = {375–387}, abstract = {In this article we investigate the effect of increasing risk aversion onutility-based prices. We are dealing with the utility indifference price (or reservationprice), defined in [12] for the first time. This is the minimal amount added toan option seller’s initial capital which allows her to attain the same utilitythatshe would have attained from her initial capital without selling the option, seeDefinition 4.2 below. Intuitively, when risk aversion tends to infinity, reservationprice should tend to the superreplication price (i.e. the price of hedging theoption without any risk).This result was shown in [19] for Brownian models and in [9] in a semi-martingale setting when the agent has constant absolute risk aversion (i.e. forexponential utility functions). Certain other classes of utility functions weretreated in [4], models with transaction costs were considered in [5].However, an extension of this result to general utility functions was lacking.In [6] and [7] the case of discrete-time markets was treated for utilities on thepositive axis as well as on the real line. Now we prove this result in a continuous-time semimartingale framework, under suitable hypotheses . In section 2 we model the agent’s preferences and introduce a growth condi-tion (related to the elasticity of utility functions), in section 3 the market modeland a compactness assumption are discussed. In section 4 the concept of utilityindifference price is formally defined and the two main theorems are proved.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In this article we investigate the effect of increasing risk aversion onutility-based prices. We are dealing with the utility indifference price (or reservationprice), defined in [12] for the first time. This is the minimal amount added toan option seller’s initial capital which allows her to attain the same utilitythatshe would have attained from her initial capital without selling the option, seeDefinition 4.2 below. Intuitively, when risk aversion tends to infinity, reservationprice should tend to the superreplication price (i.e. the price of hedging theoption without any risk).This result was shown in [19] for Brownian models and in [9] in a semi-martingale setting when the agent has constant absolute risk aversion (i.e. forexponential utility functions). Certain other classes of utility functions weretreated in [4], models with transaction costs were considered in [5].However, an extension of this result to general utility functions was lacking.In [6] and [7] the case of discrete-time markets was treated for utilities on thepositive axis as well as on the real line. Now we prove this result in a continuous-time semimartingale framework, under suitable hypotheses . In section 2 we model the agent’s preferences and introduce a growth condi-tion (related to the elasticity of utility functions), in section 3 the market modeland a compactness assumption are discussed. In section 4 the concept of utilityindifference price is formally defined and the two main theorems are proved. |

Laurence Carassus; Huyen Pham; Nizar Touzi No Arbitrage in Discrete Time Under Portfolio Constraints Article de journal 2018. @article{carassus2017b, title = {No Arbitrage in Discrete Time Under Portfolio Constraints}, author = {Laurence Carassus and Huyen Pham and Nizar Touzi}, editor = {Alfred Rényi Institute of Mathematics, Hungarian Academy of Sciences}, url = {https://arxiv.org/abs/1904.08780v2}, year = {2018}, date = {2018-10-08}, abstract = {In a discrete time and multiple-priors setting, we propose a new characterisation of the condition of quasi-sure no-arbitrage which has become a standard assumption. This characterisation shows that it is indeed a well-chosen condition being equivalent to several previously used alternative notions of no-arbitrage and allowing the proof of important results in mathematical finance. We also revisit the so-called geometric and quantitative no-arbitrage conditions and explicit two important examples where all these concepts are illustrated}, keywords = {}, pubstate = {published}, tppubtype = {article} } In a discrete time and multiple-priors setting, we propose a new characterisation of the condition of quasi-sure no-arbitrage which has become a standard assumption. This characterisation shows that it is indeed a well-chosen condition being equivalent to several previously used alternative notions of no-arbitrage and allowing the proof of important results in mathematical finance. We also revisit the so-called geometric and quantitative no-arbitrage conditions and explicit two important examples where all these concepts are illustrated |

Laurence Carassus; Tiziano Vargiolu Super-Replication Price : It can be Ok Article de journal 64 , p. 54-64, 2018. @article{Carassus2018b, title = {Super-Replication Price : It can be Ok}, author = {Laurence Carassus and Tiziano Vargiolu}, doi = {10.1051/proc/201864054 }, year = {2018}, date = {2018-10-02}, volume = {64}, pages = {54-64}, abstract = {Abstract.We consider a discrete time financial model where the support of the conditional law ofthe risky asset is bounded. For convex options we show that the super-replication problem reduces tothe replication one in a Cox-Ross-Rubinstein model whose parameters are the law support boundaries.Thus the super-replication price can be of practical use if this support is not to large. We also makethe link with the recent literature on multiple-priors models.R ́esum ́e.Nous consid ́erons un mod`ele financier `a temps discret, o`u le support de la loi conditionnellede l’actif risqu ́e est born ́e. Nous montrons, pour une option dont la fonction de paiement est convexe,que le probl`eme de surr ́eplication se r ́eduit `a un probl`eme de r ́eplication parfaite dans un mod`eleCox-Ross-Rubinstein, dont les param`etres sont les bornes du support de la loi. Ainsi, le prix desurr ́eplication peut ˆetre utilis ́e en pratique, si ce support n’est pas trop grand. Nous faisons aussi lelien avec la litt ́erature r ́ecente portant sur les mod`eles `a croyances multiples}, keywords = {}, pubstate = {published}, tppubtype = {article} } Abstract.We consider a discrete time financial model where the support of the conditional law ofthe risky asset is bounded. For convex options we show that the super-replication problem reduces tothe replication one in a Cox-Ross-Rubinstein model whose parameters are the law support boundaries.Thus the super-replication price can be of practical use if this support is not to large. We also makethe link with the recent literature on multiple-priors models.R ́esum ́e.Nous consid ́erons un mod`ele financier `a temps discret, o`u le support de la loi conditionnellede l’actif risqu ́e est born ́e. Nous montrons, pour une option dont la fonction de paiement est convexe,que le probl`eme de surr ́eplication se r ́eduit `a un probl`eme de r ́eplication parfaite dans un mod`eleCox-Ross-Rubinstein, dont les param`etres sont les bornes du support de la loi. Ainsi, le prix desurr ́eplication peut ˆetre utilis ́e en pratique, si ce support n’est pas trop grand. Nous faisons aussi lelien avec la litt ́erature r ́ecente portant sur les mod`eles `a croyances multiples |

Laurence Carassus Multiple-priors Optimal Investment for Unbounded Utility Function in Discrete Time Article de journal 28 (3), p. 1856-1892., 2018. @article{carassus2017db, title = {Multiple-priors Optimal Investment for Unbounded Utility Function in Discrete Time}, author = {Laurence Carassus}, year = {2018}, date = {2018-06-01}, booktitle = {AMAMEF, Amsterdam, juin 2017}, volume = {28}, number = {3}, pages = {1856-1892.}, abstract = {This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under nondominated model uncertainty. We use a dynamic programming framework together with measurable selection arguments to prove that under mild integrability conditions, an optimal portfolio exists for an unbounded utility function defined on the half-real line.}, keywords = {}, pubstate = {published}, tppubtype = {article} } This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under nondominated model uncertainty. We use a dynamic programming framework together with measurable selection arguments to prove that under mild integrability conditions, an optimal portfolio exists for an unbounded utility function defined on the half-real line. |

Laurence Carassus No-arbitrage and optimal investment with possibly non-concave utilities: a measure theoretical approach Article de journal Mathematical Methods of Operations Research, 88 (2), p. 241-281, 2018, ISBN: 1432-5217. @article{Carassus2018h, title = {No-arbitrage and optimal investment with possibly non-concave utilities: a measure theoretical approach}, author = {Laurence Carassus}, editor = {Springer Berlin Heidelberg}, doi = {10.1007/s00186-018-0635-3}, isbn = {1432-5217}, year = {2018}, date = {2018-03-18}, journal = {Mathematical Methods of Operations Research}, volume = {88}, number = {2}, pages = {241-281}, abstract = {We consider a discrete-time financial market model with finite time horizon and investors with utility functions defined on the non-negative half-line. We allow these functions to be random, non-concave and non-smooth. We use a dynamic programming framework together with measurable selection arguments to establish both the characterisation of the no-arbitrage property for such markets and the existence of an optimal portfolio strategy for such investors.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We consider a discrete-time financial market model with finite time horizon and investors with utility functions defined on the non-negative half-line. We allow these functions to be random, non-concave and non-smooth. We use a dynamic programming framework together with measurable selection arguments to establish both the characterisation of the no-arbitrage property for such markets and the existence of an optimal portfolio strategy for such investors. |

Laurence Carassus; Romain Blanchard Multiple-priors Optimal Investment in Discrete Time for Unbounded Utility Function Article de journal Annals of Applied Probability, 28 (3), p. 1856-1892, 2018. @article{Carassus2018e, title = {Multiple-priors Optimal Investment in Discrete Time for Unbounded Utility Function}, author = {Laurence Carassus and Romain Blanchard}, year = {2018}, date = {2018-01-02}, journal = {Annals of Applied Probability}, volume = {28}, number = {3}, pages = {1856-1892}, abstract = {Abstract This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under nondominated model uncertainty. We use a dynamic programming framework together with measurable selection arguments to prove that under mild integrability conditions, an optimal portfolio exists for an unbounded utility function defined on the half-real line.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Abstract This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under nondominated model uncertainty. We use a dynamic programming framework together with measurable selection arguments to prove that under mild integrability conditions, an optimal portfolio exists for an unbounded utility function defined on the half-real line. |

Laurence Carassus; Romain Blanchard Convergence of utility indifference prices to the superreplication price in a multiple-priors framework Article de journal 2017. @article{Carassus2017gb, title = {Convergence of utility indifference prices to the superreplication price in a multiple-priors framework}, author = {Laurence Carassus and Romain Blanchard}, year = {2017}, date = {2017-09-27}, abstract = {This paper formulates an utility indifference pricing model for investors trading in a discrete time financial market under non-dominated model uncertainty. The investors preferences are described by strictly increasing concave random functions defined on the positive axis. We prove that under suitable conditions the multiple-priors utility indifference prices of a contingent claim converge to its multiple-priors superreplication price. We also revisit the notion of certainty equivalent for random utility functions and establish its relation with the absolute risk aversion. )}, keywords = {}, pubstate = {published}, tppubtype = {article} } This paper formulates an utility indifference pricing model for investors trading in a discrete time financial market under non-dominated model uncertainty. The investors preferences are described by strictly increasing concave random functions defined on the positive axis. We prove that under suitable conditions the multiple-priors utility indifference prices of a contingent claim converge to its multiple-priors superreplication price. We also revisit the notion of certainty equivalent for random utility functions and establish its relation with the absolute risk aversion. ) |

Laurence Carassus; Huyen Pham; Nizar Touzi No Arbitrage in Discrete Time Under Portfolio Constraints Article de journal 2017. @article{carassus2017bb, title = {No Arbitrage in Discrete Time Under Portfolio Constraints}, author = {Laurence Carassus and Huyen Pham and Nizar Touzi}, editor = {Hungarian Academy Sciences of Alfred Rényi Institute of Mathematics}, year = {2017}, date = {2017-05-15}, keywords = {}, pubstate = {published}, tppubtype = {article} } |

Laurence Carassus; Miklos Rasonyi Maximization of nonconcave utility functions in discrete-time financial market models Article de journal Mathematics of Operations Research, 41 (1), p. 1-376, 2016. @article{Carassus2015e, title = {Maximization of nonconcave utility functions in discrete-time financial market models}, author = {Laurence Carassus and Miklos Rasonyi}, doi = {10.1287/moor.2015.0720}, year = {2016}, date = {2016-02-00}, journal = {Mathematics of Operations Research}, volume = {41}, number = {1}, pages = {1-376}, abstract = {This paper investigates the problem of maximizing expected terminal utility in a (generically incomplete) discrete-time financial market model with finite time horizon. By contrast to the standard setting, a possibly nonconcave utility function U is considered, with domain of definition equal to the whole real line. Simple conditions are presented that guarantee the existence of an optimal strategy for the problem. In particular, the asymptotic elasticity of U plays a decisive role: Existence can be shown when it is strictly greater at −∞ than at +∞.}, keywords = {}, pubstate = {published}, tppubtype = {article} } This paper investigates the problem of maximizing expected terminal utility in a (generically incomplete) discrete-time financial market model with finite time horizon. By contrast to the standard setting, a possibly nonconcave utility function U is considered, with domain of definition equal to the whole real line. Simple conditions are presented that guarantee the existence of an optimal strategy for the problem. In particular, the asymptotic elasticity of U plays a decisive role: Existence can be shown when it is strictly greater at −∞ than at +∞. |

Laurence Carassus; Miklos Rasonyi; Andrea M Rodrigues Non-concave utility maximisation on the positive real axis in discrete time Article de journal Mathematics and Financial Economics, 9 (4), p. 325-349, 2015. @article{Carassus2015bb, title = {Non-concave utility maximisation on the positive real axis in discrete time}, author = {Laurence Carassus and Miklos Rasonyi and Andrea M Rodrigues}, doi = {10.1007/s11579-015-0146-4}, year = {2015}, date = {2015-05-08}, journal = {Mathematics and Financial Economics}, volume = {9}, number = {4}, pages = {325-349}, abstract = {We treat a discrete-time asset allocation problem in an arbitrage-free, generically incomplete financial market, where the investor has a possibly non-concave utility function and wealth is restricted to remain non-negative. Under easily verifiable conditions, we establish the existence of optimal portfolios.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We treat a discrete-time asset allocation problem in an arbitrage-free, generically incomplete financial market, where the investor has a possibly non-concave utility function and wealth is restricted to remain non-negative. Under easily verifiable conditions, we establish the existence of optimal portfolios. |

Laurence Carassus; Guillaume Bernis; Grégoire Docq; Simone Scotti Optimal credit allocation under regime uncertainty with sensitivity analysis Article de journal International Journal of Theorical and Applied Finance, 18 (1), 2015. @article{Carassus2015db, title = {Optimal credit allocation under regime uncertainty with sensitivity analysis}, author = {Laurence Carassus and Guillaume Bernis and Grégoire Docq and Simone Scotti}, doi = {10.1142/S0219024915500028}, year = {2015}, date = {2015-01-21}, journal = {International Journal of Theorical and Applied Finance}, volume = {18}, number = {1}, abstract = {We consider the problem of credit allocation in a regime-switching model. The global evolution of the credit market is driven by a benchmark, the drift of which is given by a two-state continuous-time hidden Markov chain. We apply filtering techniques to obtain the diffusion of the credit assets under partial observation and show that they have a specific excess return with respect to the benchmark. The investor performs a simple mean–variance allocation on credit assets. However, returns and variance matrix have to be computed by a numerical method such as Monte Carlo, because of the dynamics of the system and the non-linearity of the asset prices. We use the theory of Dirichlet forms to deal with the uncertainty on the excess returns. This approach provides an estimation of the bias and the variance of the optimal allocation, and return. We propose an application in the case of a sectorial allocation with Credit Default Swaps (CDS), fully calibrated with observable data or direct input given by the portfolio manager.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We consider the problem of credit allocation in a regime-switching model. The global evolution of the credit market is driven by a benchmark, the drift of which is given by a two-state continuous-time hidden Markov chain. We apply filtering techniques to obtain the diffusion of the credit assets under partial observation and show that they have a specific excess return with respect to the benchmark. The investor performs a simple mean–variance allocation on credit assets. However, returns and variance matrix have to be computed by a numerical method such as Monte Carlo, because of the dynamics of the system and the non-linearity of the asset prices. We use the theory of Dirichlet forms to deal with the uncertainty on the excess returns. This approach provides an estimation of the bias and the variance of the optimal allocation, and return. We propose an application in the case of a sectorial allocation with Credit Default Swaps (CDS), fully calibrated with observable data or direct input given by the portfolio manager. |

Laurence Carassus; E Temam Pricing and hedging basis risk under no good deal assumption Article de journal Annals of Finance, 10 (1), p. 127-170, 2013, ISBN: 1614-2454. @article{Carassus2013bb, title = {Pricing and hedging basis risk under no good deal assumption}, author = {Laurence Carassus and E Temam}, editor = {Springer Berlin Heidelberg}, doi = {10.1007/s10436-013-0246-1}, isbn = {1614-2454}, year = {2013}, date = {2013-12-19}, journal = {Annals of Finance}, volume = {10}, number = {1}, pages = {127-170}, abstract = {We consider the problem of explicitly pricing and hedging an option written on a non-exchangeable asset when trading in a correlated asset is possible. This is a typical case of incomplete market where it is well known that the super-replication concept provides generally too high prices. We study several prices and in particular the instantaneous no-good-deal price (see Cochrane and Saa-Requejo in J Polit Econ 108(1):79–119, 2001) and the global one. We show numerically that the global no-good-deal price can be significantly higher that the instantaneous one. We then propose several hedging strategies and show numerically that the mean-variance hedging strategy can be efficient.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We consider the problem of explicitly pricing and hedging an option written on a non-exchangeable asset when trading in a correlated asset is possible. This is a typical case of incomplete market where it is well known that the super-replication concept provides generally too high prices. We study several prices and in particular the instantaneous no-good-deal price (see Cochrane and Saa-Requejo in J Polit Econ 108(1):79–119, 2001) and the global one. We show numerically that the global no-good-deal price can be significantly higher that the instantaneous one. We then propose several hedging strategies and show numerically that the mean-variance hedging strategy can be efficient. |

Laurence Carassus; Miklos Rasonyi On optimal Investment for a behavioral investor in multiperiod incomplete market models Article de journal Mathematical Finance, 25 (1), p. 115-153, 2013. @article{Carassus2013d, title = {On optimal Investment for a behavioral investor in multiperiod incomplete market models}, author = {Laurence Carassus and Miklos Rasonyi}, doi = {10.1111/mafi.12018}, year = {2013}, date = {2013-02-07}, journal = {Mathematical Finance}, volume = {25}, number = {1}, pages = {115-153}, abstract = {We study the optimal investment problem for a behavioral investor in an incomplete discrete‐time multiperiod financial market model. For the first time in the literature, we provide easily verifiable and interpretable conditions for well‐posedness. Under two different sets of assumptions, we also establish the existence of optimal strategies.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We study the optimal investment problem for a behavioral investor in an incomplete discrete‐time multiperiod financial market model. For the first time in the literature, we provide easily verifiable and interpretable conditions for well‐posedness. Under two different sets of assumptions, we also establish the existence of optimal strategies. |

Laurence Carassus; Miklos Rasonyi Optimal Strategies and Utility-Based Prices Converge When Agents’ Preferences Do Article de journal Informs, 32 (1), 2007. @article{enqRasonyi2007b, title = {Optimal Strategies and Utility-Based Prices Converge When Agents’ Preferences Do}, author = {Laurence Carassus and Miklos Rasonyi}, editor = {Informs PubsOnLine}, doi = {doi.org/10.1287/moor.1060.0220}, year = {2007}, date = {2007-02-01}, journal = {Informs}, volume = {32}, number = {1}, abstract = {Abstract A discrete-time financial market model is considered with a sequence of investors whose preferences are described by their utility functions Un, defined on the whole real line and assumed to be strictly concave and increasing. Under suitable hypotheses, it is shown that whenever Un tends to another utility function U∞, the respective optimal strategies converge, too. Under additional assumptions the rate of convergence is estimated. We also establish the continuity of the fair price of Davis [Davis, M. H. A. 1997. Option pricing in incomplete markets. M. A. H. Dempster, S. R. Pliska, eds. Mathematics of Derivative Securities. Cambridge University Press, pp. 216–226] and the utility indifference price of Hodges and Neuberger [Hodges, R., K. Neuberger. 1989. Optimal replication of contingent claims under transaction costs. Rev. Futures Markets8 222–239] with respect to changes in agents’ preferences.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Abstract A discrete-time financial market model is considered with a sequence of investors whose preferences are described by their utility functions Un, defined on the whole real line and assumed to be strictly concave and increasing. Under suitable hypotheses, it is shown that whenever Un tends to another utility function U∞, the respective optimal strategies converge, too. Under additional assumptions the rate of convergence is estimated. We also establish the continuity of the fair price of Davis [Davis, M. H. A. 1997. Option pricing in incomplete markets. M. A. H. Dempster, S. R. Pliska, eds. Mathematics of Derivative Securities. Cambridge University Press, pp. 216–226] and the utility indifference price of Hodges and Neuberger [Hodges, R., K. Neuberger. 1989. Optimal replication of contingent claims under transaction costs. Rev. Futures Markets8 222–239] with respect to changes in agents’ preferences. |

Laurence Carassus; Miklos Rasonyi Convergence of Utility Indifference Prices to the Superreplication Price Article de journal Mathematical Methods of Operations Research, 64 (1), p. 145-154, 2006, ISBN: 1432-5217. @article{Carassus2006c, title = {Convergence of Utility Indifference Prices to the Superreplication Price}, author = {Laurence Carassus and Miklos Rasonyi}, editor = {Springer-Verlag}, doi = {10.1007/s00186-006-0074-4}, isbn = {1432-5217}, year = {2006}, date = {2006-06-24}, journal = {Mathematical Methods of Operations Research}, volume = {64}, number = {1}, pages = {145-154}, abstract = {A discrete-time financial market model is considered with a sequence of investors whose preferences are described by concave strictly increasing functions defined on the positive axis. Under suitable conditions, we show that the utility indifference prices of a bounded contingent claim converge to its superreplication price when the investors’ absolute risk-aversion tends to infinity.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A discrete-time financial market model is considered with a sequence of investors whose preferences are described by concave strictly increasing functions defined on the positive axis. Under suitable conditions, we show that the utility indifference prices of a bounded contingent claim converge to its superreplication price when the investors’ absolute risk-aversion tends to infinity. |

Laurence Carassus; Elyes Jouini Investment and Arbitrage Opportunities with Short Sales Constraints Article de journal Mathematical Finance, 8 (3), p. 169-178, 2002. @article{Carassus2002b, title = {Investment and Arbitrage Opportunities with Short Sales Constraints}, author = {Laurence Carassus and Elyes Jouini}, doi = {10.1111/1467-9965.00051}, year = {2002}, date = {2002-01-05}, journal = {Mathematical Finance}, volume = {8}, number = {3}, pages = {169-178}, abstract = {In this paper we consider a family of investment projects defined by their deterministic cash flows. We assume stationarity—that is, projects available today are the same as those available in the past. In this framework, we prove that the absence of arbitrage opportunities is equivalent to the existence of a discount rate such that the net present value of all projects is nonpositive if the projects cannot be sold short and is equal to zero otherwise. Our result allows for an infinite number of projects and for continuous as well as discrete cash flows, generalizing similar results established by Cantor and Lippman (1983, 1995) and Adler and Gale (1997) in a discrete time framework and for a finite number of projects.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In this paper we consider a family of investment projects defined by their deterministic cash flows. We assume stationarity—that is, projects available today are the same as those available in the past. In this framework, we prove that the absence of arbitrage opportunities is equivalent to the existence of a discount rate such that the net present value of all projects is nonpositive if the projects cannot be sold short and is equal to zero otherwise. Our result allows for an infinite number of projects and for continuous as well as discrete cash flows, generalizing similar results established by Cantor and Lippman (1983, 1995) and Adler and Gale (1997) in a discrete time framework and for a finite number of projects. |

Laurence Carassus; Elyès Jouini A discrete stochastic model for investment with an application to the transaction costs case Article de journal Journal of Mathematical, 33 (1), p. 57-80, 2000. @article{Carassus2000b, title = {A discrete stochastic model for investment with an application to the transaction costs case}, author = {Laurence Carassus and Elyès Jouini}, editor = {ELSEVIER}, doi = {10.1016/S0304-4068(99)00005-1}, year = {2000}, date = {2000-02-05}, journal = {Journal of Mathematical}, volume = {33}, number = {1}, pages = {57-80}, abstract = {This work consists of two parts. In the first one, we study a model where the assets are investment opportunities, which are completely described by their cash-flows. Those cash-flows follow some binomial processes and have the following property called stationarity: it is possible to initiate them at any time and in any state of the world at the same condition. In such a model, we prove that the absence of arbitrage condition implies the existence of a discount rate and a particular probability measure such that the expected value of the net present value of each investment is non-positive if there are short-sales constraints and equal to zero otherwise. This extends the works of Cantor–Lippman [Cantor, D.G., Lippman, S.A., 1983. Investment selection with imperfect capital markets. Econometrica 51, 1121–1144; Cantor, D.G., Lippman, S.A., 1995. Optimal investment selection with a multitude of projects. Econometrica 63 (5) 1231–1241.], Adler–Gale [Alder, I., Gale, D., 1997. Arbitrage and growth rate for riskless investments in a stationary economy. Mathematical Finance 2, 73–81.] and Carassus–Jouini [Carassus, L., Jouini, E., 1998. Arbitrage and investment opportunities with short sales constraints. Mathematical Finance 8 (3) 169–178.], who studied a deterministic setup. In the second part, we apply this result to a financial model in the spirit of Cox–Ross–Rubinstein [Cox, J.C., Ross, S.A., Rubinstein, M., 1979. Option pricing: a simplified approach. Journal of Financial Economics 7, 229–264.] but where there are transaction costs on the assets. This model appears to be stationary. At the equilibrium, the Cox–Ross–Rubinstein's price of a European option is always included between its buying and its selling price. Moreover, if there is transaction cost only on the underlying asset, the option price will be equal to the Cox–Ross–Rubinstein's price. Those results give more information than the results of Jouini–Kallal [Jouini, E., Kallal, H., 1995. Martingales and arbitrage in securities markets with transaction costs. Journal of Economic Theory 66 (1) 178–197.], which where working in a finite horizon model.}, keywords = {}, pubstate = {published}, tppubtype = {article} } This work consists of two parts. In the first one, we study a model where the assets are investment opportunities, which are completely described by their cash-flows. Those cash-flows follow some binomial processes and have the following property called stationarity: it is possible to initiate them at any time and in any state of the world at the same condition. In such a model, we prove that the absence of arbitrage condition implies the existence of a discount rate and a particular probability measure such that the expected value of the net present value of each investment is non-positive if there are short-sales constraints and equal to zero otherwise. This extends the works of Cantor–Lippman [Cantor, D.G., Lippman, S.A., 1983. Investment selection with imperfect capital markets. Econometrica 51, 1121–1144; Cantor, D.G., Lippman, S.A., 1995. Optimal investment selection with a multitude of projects. Econometrica 63 (5) 1231–1241.], Adler–Gale [Alder, I., Gale, D., 1997. Arbitrage and growth rate for riskless investments in a stationary economy. Mathematical Finance 2, 73–81.] and Carassus–Jouini [Carassus, L., Jouini, E., 1998. Arbitrage and investment opportunities with short sales constraints. Mathematical Finance 8 (3) 169–178.], who studied a deterministic setup. In the second part, we apply this result to a financial model in the spirit of Cox–Ross–Rubinstein [Cox, J.C., Ross, S.A., Rubinstein, M., 1979. Option pricing: a simplified approach. Journal of Financial Economics 7, 229–264.] but where there are transaction costs on the assets. This model appears to be stationary. At the equilibrium, the Cox–Ross–Rubinstein's price of a European option is always included between its buying and its selling price. Moreover, if there is transaction cost only on the underlying asset, the option price will be equal to the Cox–Ross–Rubinstein's price. Those results give more information than the results of Jouini–Kallal [Jouini, E., Kallal, H., 1995. Martingales and arbitrage in securities markets with transaction costs. Journal of Economic Theory 66 (1) 178–197.], which where working in a finite horizon model. |

## Livres |

Laurence Carassus Probabilités : cours, exercices et problèmes corrigés Livre 2018, ISBN: ISBN-13 / 978-2807313200. @book{Carassus2018f, title = {Probabilités : cours, exercices et problèmes corrigés}, author = {Laurence Carassus }, editor = {Éditions De Boeck }, url = {https://www.deboecksuperieur.com/ouvrage/9782807313200-probabilites}, isbn = {ISBN-13 / 978-2807313200}, year = {2018}, date = {2018-09-30}, number = {368 pages}, keywords = {}, pubstate = {published}, tppubtype = {book} } |

Laurence Carassus; Gilles Pages Finance de marché: Modèles mathématiques à temps discret Livre 2015, ISBN: 978-2-311-40166-0. @book{Carassus2015cb, title = {Finance de marché: Modèles mathématiques à temps discret}, author = {Laurence Carassus and Gilles Pages}, editor = {Vuibert}, isbn = {978-2-311-40166-0}, year = {2015}, date = {2015-06-01}, keywords = {}, pubstate = {published}, tppubtype = {book} } |

## Conférences |

Laurence Carassus Mini-symposium Big Data Mégadonnées : quelques enjeux 5500 - 5599 Conférence organisation du minisymposium industriel Big Data au SMAI et modérateur de l’exposé Moulines, 2017. @conference{carassus2017cb, title = {Mini-symposium Big Data Mégadonnées : quelques enjeux}, author = {Laurence Carassus}, year = {2017}, date = {2017-06-15}, booktitle = {organisation du minisymposium industriel Big Data au SMAI et modérateur de l’exposé Moulines}, keywords = {}, pubstate = {published}, tppubtype = {conference} } |

Laurence Carassus; Simone Scotti Stochastic Sensitivity Study for Optimal Credit Allocation 5500 - 5599 Conférence 5 , Pekin University Series in Mathematics 2014. @conference{Carassus2014b, title = {Stochastic Sensitivity Study for Optimal Credit Allocation}, author = {Laurence Carassus and Simone Scotti}, editor = {World Scientific Publishing Co Pte Ltd}, doi = {10.1142/9789814602075_0008}, year = {2014}, date = {2014-00-00}, volume = {5}, pages = {147-168}, organization = {Pekin University Series in Mathematics}, abstract = {In this paper we propose a short overview of error calculus theory using Dirichlet forms which was developed by Bouleau. Then we apply this method to an optimal credit allocation problem. The study of uncertainties propagation from the parameters to the model outputs is an old topic which is generally treated following two alternative approaches. The uncertainties can be seen as infinitely small deterministic quantities. This allows to calculate the uncertainties propagation}, keywords = {}, pubstate = {published}, tppubtype = {conference} } In this paper we propose a short overview of error calculus theory using Dirichlet forms which was developed by Bouleau. Then we apply this method to an optimal credit allocation problem. The study of uncertainties propagation from the parameters to the model outputs is an old topic which is generally treated following two alternative approaches. The uncertainties can be seen as infinitely small deterministic quantities. This allows to calculate the uncertainties propagation |

Laurence Carassus; Huyen Pham Portfolio optimization for piecewise concave criteria functions (the 8th workshop on stochastic numerics) 5500 - 5599 Conférence 1620 , Kyoto university 2009. @conference{Carassus2009b, title = {Portfolio optimization for piecewise concave criteria functions (the 8th workshop on stochastic numerics)}, author = {Laurence Carassus and Huyen Pham}, editor = {Departmental Bulletin Paper}, url = {http://hdl.handle.net/2433/140221}, year = {2009}, date = {2009-01-02}, volume = {1620}, pages = {81-108}, organization = {Kyoto university}, abstract = {数理解析研究所講究録 (2009), 1620: 81-108 In the context of a complete financial model, we study the portfolio optimization problem when the objective function may have a change of concavity at a given positive constant level. This typically includes utility maximization of terminal wealth when the agent modifies her preference structure from a certain level of wealth. This also allows to consider the portfolio management problem of an investor willing to achieve a given level of performance by penalizing net loss and maximizing net gain. We finally compare some of our results with the classical portfolio choice problem of Merton by doing some numerical experiments.}, keywords = {}, pubstate = {published}, tppubtype = {conference} } 数理解析研究所講究録 (2009), 1620: 81-108 In the context of a complete financial model, we study the portfolio optimization problem when the objective function may have a change of concavity at a given positive constant level. This typically includes utility maximization of terminal wealth when the agent modifies her preference structure from a certain level of wealth. This also allows to consider the portfolio management problem of an investor willing to achieve a given level of performance by penalizing net loss and maximizing net gain. We finally compare some of our results with the classical portfolio choice problem of Merton by doing some numerical experiments. |

Laurence Carassus; Emmanuel Gobet; E Teman A Class of Financial Products and Models Where Super-replication Prices are Explicit 5500 - 5599 Conférence 2006, ISBN: 9789812704139. @conference{Carassus2006bb, title = {A Class of Financial Products and Models Where Super-replication Prices are Explicit}, author = {Laurence Carassus and Emmanuel Gobet and E Teman}, doi = {10.1142/9789812770448_0004}, isbn = {9789812704139}, year = {2006}, date = {2006-03-06}, journal = {Stochastic Processes and Applications to Mathematical Finance,}, pages = {67-84}, abstract = {This volume contains the contributions to a conference that is among the most important meetings in financial mathematics. Serving as a bridge between probabilists in Japan (called the Ito School and known for its highly sophisticated mathematics) and mathematical finance and financial engineering, the conference elicits the very highest quality papers in the field of financial mathematics.}, keywords = {}, pubstate = {published}, tppubtype = {conference} } This volume contains the contributions to a conference that is among the most important meetings in financial mathematics. Serving as a bridge between probabilists in Japan (called the Ito School and known for its highly sophisticated mathematics) and mathematical finance and financial engineering, the conference elicits the very highest quality papers in the field of financial mathematics. |

## Book Chapters |

Laurence Carassus Apprendre de Léonard - Léonard De Vinci : L'art de la formule Book Chapter 2019, ISBN: 978-2-9570634-0-6. @inbook{Carassus2019c, title = {Apprendre de Léonard - Léonard De Vinci : L'art de la formule}, author = {Laurence Carassus }, url = {https://www.esilv.fr/leonard-de-vinci%E2%80%AF-lart-de-la-formule/}, isbn = {978-2-9570634-0-6}, year = {2019}, date = {2019-11-07}, keywords = {}, pubstate = {published}, tppubtype = {inbook} } |

## inproceedings |

Laurence Carassus; Miklos Rasonyi From small markets to big markets Inproceedings 2019. @inproceedings{Carassus2019bb, title = {From small markets to big markets}, author = {Laurence Carassus and Miklos Rasonyi}, year = {2019}, date = {2019-07-12}, abstract = {We study the most famous example of a large financial market: the Arbitrage Pricing Model, where investors can trade in a one-period setting with countably many assets admitting a factor structure. We consider the problem of maximising expected utility in this setting. Besides establishing the existence of optimizers under weaker assumptions than previous papers, we go on studying the relationship between optimal investments in finite market segments and those in the whole market. We show that certain natural (but nontrivial) continuity rules hold: maximal satisfaction, reservation prices and (convex combinations of) optimizers computed in small markets converge to their respective counterparts in the big market.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We study the most famous example of a large financial market: the Arbitrage Pricing Model, where investors can trade in a one-period setting with countably many assets admitting a factor structure. We consider the problem of maximising expected utility in this setting. Besides establishing the existence of optimizers under weaker assumptions than previous papers, we go on studying the relationship between optimal investments in finite market segments and those in the whole market. We show that certain natural (but nontrivial) continuity rules hold: maximal satisfaction, reservation prices and (convex combinations of) optimizers computed in small markets converge to their respective counterparts in the big market. |

Laurence Carassus; Julien Baptiste; Emmanuel Lépinette Pricing Without Martingale Measure Inproceedings Springer-Verlag, (Ed.): 2019. @inproceedings{Carassus2018db, title = {Pricing Without Martingale Measure}, author = {Laurence Carassus and Julien Baptiste and Emmanuel Lépinette}, editor = {Springer-Verlag}, url = {https://arxiv.org/abs/1807.04612}, doi = {10.2139/ssrn.3190878}, year = {2019}, date = {2019-05-10}, abstract = {For several decades, the no-arbitrage (NA) condition and the martingale measures have played a major role in the financial asset's pricing theory. Here, we propose a new approach based on convex duality instead of martingale measures duality: our prices will be expressed using Fenchel conjugate and bi-conjugate. This naturally leads to a weak condition of absence of arbitrage opportunity, called Absence of Immediate Profit (AIP), which asserts that the price of the zero claim should be zero. We study the link between (AIP), (NA) and the no-free lunch condition. We show in a one step model that, under (AIP), the super-hedging cost is just the payoff's concave envelop and that (AIP) is equivalent to the non-negativity of the super-hedging prices of some call option. In the multiple-period case, for a particular, but still general setup, we propose a recursive scheme for the computation of a the super-hedging cost of a convex option. We also give some numerical illustrations.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } For several decades, the no-arbitrage (NA) condition and the martingale measures have played a major role in the financial asset's pricing theory. Here, we propose a new approach based on convex duality instead of martingale measures duality: our prices will be expressed using Fenchel conjugate and bi-conjugate. This naturally leads to a weak condition of absence of arbitrage opportunity, called Absence of Immediate Profit (AIP), which asserts that the price of the zero claim should be zero. We study the link between (AIP), (NA) and the no-free lunch condition. We show in a one step model that, under (AIP), the super-hedging cost is just the payoff's concave envelop and that (AIP) is equivalent to the non-negativity of the super-hedging prices of some call option. In the multiple-period case, for a particular, but still general setup, we propose a recursive scheme for the computation of a the super-hedging cost of a convex option. We also give some numerical illustrations. |

Laurence Carassus; Miklos Rasonyi Risk-neutral pricing for APT Inproceedings 2019. @inproceedings{Carassus2019g, title = {Risk-neutral pricing for APT}, author = {Laurence Carassus and Miklos Rasonyi}, year = {2019}, date = {2019-04-25}, abstract = {We consider the problem of super-replication (hedging without risk) for the Arbitrage Pricing Theory. The dual characterization of super-replication cost is provided. It is shown that the reservation prices of investors converge to this cost as their respective risk-aversion tends to infinity.}, keywords = {}, pubstate = {published}, tppubtype = {inproceedings} } We consider the problem of super-replication (hedging without risk) for the Arbitrage Pricing Theory. The dual characterization of super-replication cost is provided. It is shown that the reservation prices of investors converge to this cost as their respective risk-aversion tends to infinity. |

## Divers |

Laurence Carassus; M.Guidoux; M.Gourand; D.D. Barkat Pilier 2 Bâle II, les fonds propres économiques : surmonter les difficultés méthodologiques Divers Lettre des Services Financiers, 2007. @misc{Carassus2007, title = {Pilier 2 Bâle II, les fonds propres économiques : surmonter les difficultés méthodologiques}, author = {Laurence Carassus and M.Guidoux and M.Gourand and D.D. Barkat}, year = {2007}, date = {2007-06-30}, howpublished = {Lettre des Services Financiers}, keywords = {}, pubstate = {published}, tppubtype = {misc} } |

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