ANAlYSIS 0F INCOMPLETE STOCK MARKET WITH JUMP—DIFFUSION UNCERTAINTY

This paper studies incomplete stock market that includes discontinuous price processes.The discontinuity is modeled by very general point processes admitting only stochastic intensities.Prices are driven by jump-diffusion uncertainty and have random but predictable jumps.The space of risk-neutral measures the are associated with the market is identified and related to fictitious completions.The construction of replicating portfolios if discussed,and convex duality methods are used to prove existence of optimal consumption and investment policies for a problem of utility maximization.