Abstract (EN)

In this paper, we focus on the following problem: given a financial market, modelled by a process S=(St)t∈T, and a family MN={μt1,…,tN:t1,…,tN∈T} of probability measures on B(RN), with N a positive integer and T the time space, we search for financially meaningful conditions which are equivalent to the existence and uniqueness of an equivalent (local) martingale measure (EMM) Q such that the price process S has under Q the pre-specified finite-dimensional distributions of order N (N-dds) MN. We call these two equivalent properties, respectively, N -mixed no free lunch and market N -completeness. They are based on a classification of contingent claims with respect to their path-dependence on S and on the related notion of N-mixed strategy. Finally, we apply this approach to the Black-Scholes model with jumps, by showing a uniqueness result for its equivalent martingale measures set.