An Approximation Algorithm for Optimal Consumption/Investment Problems

Abstract

This article develops a simple approach to solving continuous-time portfolio choice problems. Portfolio problems for which no closed-form solutions are available may be handled by this technique, which substitutes the numerical solution of partial differential equations with a non-linear numerical algorithm approximating the solution. This paper complements the wide literature in economics on the solution of dynamic problems in dicrete time. The algorithm is parismonious, and is illustrated by solving two examples, one, the standard Merton problem, and two, a jump-diffusion problem.