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Pricing without martingale measure

Baptiste, Julien; Carassus, Laurence; Lépinette, Emmanuel (2018), Pricing without martingale measure. https://basepub.dauphine.fr/handle/123456789/17961

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BCL-First-16-04-18.pdf (471.1Kb)
Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-01774150
Date
2018
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
31
Metadata
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Author(s)
Baptiste, Julien cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Carassus, Laurence
Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Lépinette, Emmanuel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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 is lead naturally 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.
Subjects / Keywords
Financial market models; Super-hedging prices; No-arbitrage condition; Conditional support; Essential supremum

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