English
Pricing without martingale measure
Multi angle
Auteurs : Carassus, Laurence (Auteur de la conférence)
CIRM (Editeur )
49N15 - Duality theory
60G42 - Martingales with discrete parameter
90C15 - Stochastic programming
91G10 - Portfolio theory
CIRM (Editeur )
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Résumé :
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 biconjugate.
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.
Mots-Clés : financial market models; super-hedging prices; no-arbitrage condition; conditional support; essential suprenum
Codes MSC : 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.
Mots-Clés : financial market models; super-hedging prices; no-arbitrage condition; conditional support; essential suprenum
49N15 - Duality theory
60G42 - Martingales with discrete parameter
90C15 - Stochastic programming
91G10 - Portfolio theory
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de Publication : 18/09/2018 Date de Captation : 06/09/2018 Sous Collection : Research talks Catégorie arXiv : Mathematical Finance Domaine(s) : Probabilités & Statistiques Format : MP4 (.mp4) - HD Durée : 00:33:25 Audience : Chercheurs Download : https://videos.cirm-math.fr/2018-09-06_Carassus.mp4 
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Informations sur la Rencontre
Nom de la Rencontre : Innovative Research in Mathematical Finance / Recherche innovante en mathématiques financièresOrganisateurs de la Rencontre : Callegaro, Giorgia ; Jeanblanc, Monique ; Lépinette, Emmanuel ; Molchanov, Ilya ; Schweizer, Martin ; Touzi, Nizar Dates : 03/09/2018 - 07/09/2018 Année de la rencontre : 2018 URL de la Rencontre : https://conferences.cirm-math.fr/1816.html
Données de citation
DOI : 10.24350/CIRM.V.19444203Citer cette vidéo: Carassus, Laurence (2018). Pricing without martingale measure. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19444203 URI : http://dx.doi.org/10.24350/CIRM.V.19444203 |
Voir Aussi
- [Multi angle] Set-valued risk measures of non-convex portfolios / Auteur de la conférence Molchanov, Ilya.
- [Multi angle] Discounting invariant FTAP for large financial markets / Auteur de la conférence Balint, Daniel.
- [Multi angle] From multivariate quantiles to set-valued risk measures: a set optimization - approach to financial models with frictions / Auteur de la conférence Hamel, Andreas H..
- [Post-edited] Approximation and calibration of laws of solutions to stochastic differential equations / Auteur de la conférence Bion-Nadal, Jocelyne.
Bibliographie
- E. N. Barron, P. Cardaliaguet, and R. Jensen, Conditional Essential Suprema with Applications, Applied Mathematics and Optimization, vol.48, issue.3, pp.229-253, 2003 - https://dx.doi.org/10.1007/s00245-003-0776-4
- J. Baptiste, L. Carassus, & E. Lépinette. Pricing without martingale measure - https://arxiv.org/abs/1807.04612
- B. Bensaid, J. P. Lesne, H. Pagès, and J. Scheinkman, Derivate asset pricing with transaction costs, Mathematical Finance, vol.15, issue.4, pp.63-86, 1992 - https://dx.doi.org/10.2307/2328113
- L. Carassus, E. Gobet, and E. Temam, A Class of Financial Products and Models Where Super-replication Prices are Explicit, Stochastic Processes and Applications to Mathematical Finance, 2006 - https://dx.doi.org/10.1142/9789812770448_0004
- A. S. Cherny, Pricing with Coherent Risk, Theory of Probability & Its Applications, vol.52, issue.3, pp.389-415 - https://dx.doi.org/10.1137/S0040585X97983158
- E. C. Dalang, A. Morton, and W. Willinger, Equivalent martingale measures and no-arbitrage in stochastic securities market models, Stochastics and Stochastic Reports, vol.19, issue.2, pp.185-201, 1990 - https://dx.doi.org/10.1017/S0001867800016360
- F. Delbaen and W. Schachermayer, The Mathematics of Arbitrage, 2006 - http://dx.doi.org/10.1007/978-3-540-31299-4
- H. Föllmer and D. Kramkov, Optional Decompositions under Constraints, Probability Theory and Related Fields, pp.1-25, 1997 - http://dx.doi.org/10.1007/s004400050122
- J. M. Harrison and D. M. Kreps, Martingales and arbitrage in multiperiod securities markets, Journal of Economic Theory, vol.20, issue.3, pp.381-408, 1979 - https://dx.doi.org/10.1016/0022-0531(79)90043-7
- J. M. Harrison and S. Pliska, Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and their Applications, pp.215-260, 1981 - https://dx.doi.org/10.1016/0304-4149(81)90026-0
- C. Hess, Set-valued integration and set-valued probability theory: An overview, Handbook of Measure Theory, pp.617-673, 2002 - https://doi.org/10.1016/B978-044450263-6/50015-4
- Y. Kabanov and M. Safarian, Markets with transaction costs. Mathematical Theory, 2009 - https://dx.doi.org/10.1007/978-3-540-68121-2
- Y. Kabanov and E. Lépinette, Essential supremum with respect to a random partial order, Journal of Mathematical Economics, vol.49, issue.6, pp.478-487, 2013 - https://dx.doi.org/10.1016/j.jmateco.2013.07.002
- D. Kreps, Arbitrage and equilibrium in economies with infinitely many commodities, Journal of Mathematical Economics, vol.8, issue.1, pp.15-35, 1981 - https://dx.doi.org/10.1016/0304-4068(81)90010-0
- E. Lépinette and I. Molchanov, Conditional cores and conditional convex hulls of random sets - https://arxiv.org/abs/1711.10303v1
- E. Lépinette and T. Tran, Approximate Hedging in a Local Volatility Model with Proportional Transaction Costs, Applied Mathematical Finance, vol.342, issue.4, pp.313-341, 2014 - https://dx.doi.org/10.1214/aoap/1060202836
- G. N. Milstein, The Probability Approach to Numerical Solution of Nonlinear Parabolic Equations. Numerical methods for partial differential equations, pp.490-522, 2002 - https://doi.org/10.1002/num.10020
- R. T. Rockafellar, Convex analysis, 1972 - https://dx.doi.org/10.1515/9781400873173
- R. T. Rockafellar and R. J. Wets, Variational analysis, Grundlehren der Mathematischen Wissenschaften, 1998 - https://dx.doi.org/10.1007/978-3-642-02431-3
