Measure of Investment Optimal Strategy

Abstract

In this paper, we considered the different strategies that generate the optimal wealth on investment. The strategy examine depends on the utility function an investor is willing to adopt, say H * at time N in every 2n possible states; in an N period setting. Negative exponential, logarithm, square root and power utility functions were established, as the market structures changed according to a Markov chain through a martingale approach. The problem of maximization is solved via Lagrange method. The performance of the investment from day-today is driven by the ratio of the risk neutral probability and the probability of rising to falling.