Uncertain Stochastic Optimal Control with Jump and Its Application in a Portfolio Game

This article describes a class of jump-uncertain stochastic control systems, and derives an Itô–Liu formula with jump. We characterize optimal law, that satisfies the Hamilton–Jacobi–Bellman equation Then, this paper deduces portfolio game under uncertain financial markets The information players is symmetrical. market constituted risk-free asset risky whose price process subjected to Black–Scholes model. formulated by two utility maximization problems, each investor tries maximize his relative utility, which weighted average terminal wealth difference between competitor. Finally, explicit expressions equilibrium investment strategies value functions for constant absolute risk-averse function are derived using dynamic programming principle.