Optimization Of Investment Returns With N-Step Utility Functions

Abstract

In this paper, we examine different ways of allocating investments, maximizing and generating optimal wealth of investment returns with N-step utility functions; in an N period setting where the investor maximizes the expected utility of the terminal wealth in a stochastic market with different utility functions. The specific utility functions considered are negative exponential, logarithm, square root and power structures as the market state changes according to a Markov chain. The states of the market describe the prevailing economic, financial, social and other conditions that affect the deterministic parameters of the models using martingale approach to obtain the optimal solution. Thus, we determine the optimization strategies for investment returns in situations where investors at different utility functions could end up doubling or halving their stake. The performance of any utility function is determined by the ratio q : q' of the probability of rising to falling as well as the ratio p : p' of the risk neutral probability measure of rising to the falling.