Optimal investment and consumption for Ornstein-Uhlenbeck spread financial markets with power utility

We consider a spread financial market defined by the Ornstein-Uhlenbeck (OU) process. We construct the optimal consumption/investment strategy for the power utility function. We study the Hamilton-Jacobi-Bellman (HJB) equation by the Feynman-Kac (FK) representation. We show the existence and uniqueness theorem for the classical solution. We study the numeric approximation and we establish the convergence rate. It turns out that in this case the convergence rate for the numerical scheme is super geometrical, i.e., more rapid than any geometrical one.