Utility-Indifference Hedging and Valuation via Reaction-Diffusion Systems

This article studies the exponential utility-indifference approach to the valuation and hedging problem in incomplete markets. We consider a financial model which is driven by a system of interacting Itô and point processes. The model allows for a variety of mutual stochastic dependencies between the tradable and non-tradable factors of risk, but still permits for a constructive and fairly explicit solution. In analogy to the Black-Scholes model, the utility based price and the hedging strategy can be described by a partial differential equation. But the non-tradable factors of risk in our model demand for an interacting semilinear system of parabolic partial differential equations. To obtain the solution for the underlying utility maximization problem, we use a verification theorem to identify the optimal martingale measure for the corresponding dual problem.