A computational scheme for the optimal strategy in an incomplete market

We examine the optimal portfolio selection problem of a single agent who receives an unhedgeable endowment. The agent wishes to optimize his/her log-utility derived from his/her terminal wealth. We do not solve this problem analytically but construct a recursive computational algorithm which approximates the optimal one. We present an 'intelligent' initial portfolio which requires, numerically, about 25% fewer corrective steps in the algorithm than a random initial portfolio, and outperforms the portfolio which ignores the unhedgeable risk of the endowment.