Université Paris 6
Pierre et Marie Curie | Université Paris 7
Denis Diderot | |

CNRS U.M.R. 7599
| ||

``Probabilités et Modèles Aléatoires''
| ||

**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
**