Minimal entropy martingale measures of jump type price processes in incomplete assets markets

We consider the incomplete assets market and assume that the market has no-arbitrage. Then there are many equivalent martingale measures associated with the market. Among them, a probability measure which minimizes the relative entropy with respect to the original probability measure P, has a special importance. Such a measure is called the minimal entropy martingale measure (MEMM). In a previous paper, we have proved the existence theorem of the MEMM for the price processes given in the form of the diffusion type stochastic differential equation. In this article we discuss the MEMM of the jump type price processes, or especially of the log Lévy processes, and we give the explicit form of MEMM. © 1999 Kluwer Academic Publishers.