  In this paper we consider a pairs trading financial market with the spread of
risky assets defined by the Ornstein-Uhlenbeck (OU) process. We implement an
optimal strategy for power utility functions for investment/consumption
problem. Through the Feynman-Kac (FK) method, we study the
Hamilton-Jacobi-Bellman (HJB) equation for this problem. Moreover, the
existence and uniqueness has been shown for classical solution for the HJB
equation. In addition, the numeric approximation for the solution of the HJB
equation has been studied and the convergence rate has been established and it
is been found that the convergence rate is extremely explosive.
