Optimal consumption problem in the Vasicek model

Abstract

We consider the problem of an optimal consumption strategy on the infinite time horizon based on the hyperbolic absolute risk aversion utility when the interest rate is an Ornstein-Uhlenbeck process. Using the method of subsolution and supersolution we obtain the existence of solutions of the dynamic programming equation. We illustrate the paper with a numerical example of the optimal consumption strategy and the value function.

Keywords

• stochastic control
• interest rate model
• optimal consumption
• HJB equation