Consumption Optimization and Equilibrium

Abstract

This paper studies the problem of consumption optimization and equilibrium in discontinuous time financial markets. It is established that the behavior model
of the stock pricing process is jump-diffusion driven by a count process. It is proved that the existence of unique optimal consumption and portfolio pair and unique equivalent martingale measure by stochastic analysis methods. The unique equivalent martingale measure, the unique optimal consumption and portfolio pair and the corresponding wealth process are deduced. Finally we provide a simple characterization of an equilibrium market.