Andersson, AngelicaElias, OlofKarlsson, JakobSvensson, Johanna2012-06-262012-06-262012-06-26http://hdl.handle.net/2077/29462In 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.engText