  In this paper, we investigate an optimal investment and consumption problem
for an investor who trades in a Black--Scholes financial market with stochastic
coefficients driven by a non-Gaussian Ornstein--Uhlenbeck process. We assume
that an agent makes investment 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 nonlinear (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.
