Submitted to the Annals of Applied Probability OPTIMAL INVESTMENT AND CONSUMPTION IN A BLACK-SCHOLES MARKET WITH LÉVY-DRIVEN STOCHASTIC COEFFICIENTS

In this paper we investigate an optimal investment and consump-tion problem for an investor who trades in a Black-Scholes finan-cial market with stochastic coefficients driven by a non-Gaussian Ornstein-Uhlenbeck process. We assume that an agent makes invest-ment and consumption decisions based on a power utility function. By applying the usual separation method in the variables, we are faced with the problem of solving a non-linear (semilinear) first-order partial integro-differential equation. A candidate solution is derived via the Feynman-Kac representation. By using the properties of an operator, defined in a suitable function space, we prove uniqueness and smoothness of the solution. Optimality is verified by applying a classical verification theorem. 1. Introduction.