Analysis of incomplete stock market with jump-diffusion uncertainty
This paper studies an incomplete stock market that includes discontinuous prices processes. The discontinuity is modelled by very general point processes admitting only stochastic intensities. Prices are driven by a jump-diffusion uncertainty and have random but predictable jumps. The space of risk-neutral measures that are associated with the market is identified and related to fictitious completions. The construction of replicating portfolios is discussed, and convex duality methods are used to prove the existence of an optimal consumption and investment policies for a problem of the utility maximization.
scientific article; zbMATH DE number 1895573