Numerical Methods for an Optimal Investment-Consumption Model

This paper examines some numerical techniques for an investment/consumption problem considered by Fleming and Zariphopoulou. The value function v(x) satisfies the differential equation of dynamic programming for x > 0. Special monotonicity and concavity features of the problem allow us to prove convergence not only of discrete approximations to v(x), but of the corresponding discrete approximations to optimal investment and consumption policies.