Finite Horizon Portfolio Selection

Abstract

We study the problem of maximising expected utility of terminal wealth over a nite horizon, with one risky and one riskless asset available, and with trades in the risky asset subject to proportional transaction costs. In a discrete time setting, using a utility function with hyperbolic risk aversion, we prove that the optimal trading strategy is characterised by a function of time (t), which represents the ratio of wealth held in the risky asset to that held in the riskless asset. There is a time varying no transaction region with boundaries b(t) < s(t), such that the portfo- lio is only rebalanced when (t) is outside this region. The results are consistent with similar studies of the in nite horizon problem with in- termediate consumption, where the no transaction region has a similar, but time independent, characterisation. We solve the problem numerically and compute the boundaries of the no transaction region for typical model parameters. We show how the results can be used to implement option pricing models with transaction costs based on utility maximisation over a nite horizon