Université Paris 6Pierre et Marie Curie Université Paris 7Denis Diderot CNRS U.M.R. 7599 Probabilités et Modèles Aléatoires''

### Financial markets with given marginals via fundamental theorems of asset pricing

Auteur(s):

Code(s) de Classification MSC:

• 60G48 Generalizations of martingales
• 90A09 Finance, portfolios, investment

Résumé: The aim of this paper is to find some financially meaningful conditions which are equivalent to the existence and uniqueness of an equivalent martingale measure $Q$ such that the price process $S$ has under $Q$ the prespecified marginals $\mathbf{M}_{J,N}$ (of order $N$). We named these two equivalent conditions, respectively, no-free lunch under $\mathbf{M}_{J,N}$ and market completeness under $\mathbf{M}_{J,N}$. They are based on a classification of contingent claims with respect to their dependence on the price process of the underlying asset. Finally, we show that for the Black-Scholes model with jumps, the set of equivalent martingale measures with given marginals of order 1 reduces to a singleton.

Mots Clés: marginals ; no-free lunch ; market completeness ; path-dependency ; Black-Scholes model with jumps

Date: 2002-10-23

Prépublication numéro: PMA-766

Pdf file : PMA-766.pdf