A Forward-Solving Numerical Technique for Dynamic Consumption and Portfolio Allocation Problems

Abstract

This paper develops a simple approach to solving multi-period consumption and investment problems. All numerical methods in use for these types of problems work by solving the problem backward, i.e., solving the consumption and investment decision at the end of the investment horizon and working backward. For certain problems, such as economies with capital gains taxes, a backward approach is extremely unwieldy. For this reason, this paper develops a forward-solving approach that is based on Monte Carlo simulations. We demonstrate that the methodology in this paper is extremely effective at solving the tax problem and other unwieldy problems. In addition, the methodology works perfectly well with problems that have traditionally used a backward-solving approach.

Keywords: Numerical, Consumption, Portfolio Choice, Asset Allocation

JEL Classification: G11, G12