The optimal consumption problem. A numerical simulation of the value function with the presence of a random income flow.

Abstract

In this thesis two methods are used to solve the optimal consumption problem. The optimal consumption problem is a well known problem in mathematical nance which in its original form was solved by Robert Merton. This report considers an extension with a presence of a random income ow. The problem is approximately solved using two numerical methods, the approximating Markov chain approach and the in nite series expansion. The Markov chain approach is a general method developed for stochastic control theory whereas the in nite series expansion method only can be applied to a speci c set of problems. In the thesis the methods are implemented and compared using MATLAB. The methods seem to complement each other well however the results are somewhat inconclusive.