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.
Keywords : 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.
Keywords : 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 arXiv category : Mathematical Finance Domaine : Probability & Statistics Format : MP4 (.mp4) - HD Durée : 00:33:25 Audience : Researchers 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 Congrès : 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.
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