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 Ito 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 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 (PDE). But the non-tradable factors of risk in our model demand an interacting semi-linear system of parabolic PDEs. 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.