An approximation algorithm for optimal consumption/investment problems

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 discrete time using projection methods. Our approach extends the approximation function to power forms, which are shown to fit finance type problems well. The algorithm is parsimonious, and is first illustrated by solving two basic examples, first, the standard Merton problem, and second, a jump‐diffusion problem. Then, we demonstrate that the model is easy to implement on a larger scale, by optimizing a portfolio of six stock indexes, and stochastic volatility driven by two correlated state variables. Copyright © 2002 John Wiley & Sons, Ltd.