Numerical methods for optimal investment-consumption models

Some stochastic control problems are considered which arise in an optimal investment-consumption context. These problems have the common feature that the optimal cost function, which satisfies a dynamic programming differential equation, is a concave function of the state. The purpose is to find good numerical approximations to the optimal cost function, as well as optimal investment and consumption policies, and to prove convergence of these approximations as the step size tends to zero. The special linear-concave structure of the problems results in stronger convergence than for more general classes of optimal stochastic control problems. The stronger convergence is obtained by partial differential equation viscosity solution methods rather than by the probabilistic-weak convergence techniques. It is expected that the methods developed with be applicable to wider classes of problems with linear-concave structure