TITLE:
Measure of Investment Optimal Strategy
AUTHORS:
J. T. Eghwerido, E. Ekuma-Okereke, E. Ekuma-Okereke, E. Efe-Eyefia, Edwin Iguodala, T. O. Obilade
KEYWORDS:
Martingale, Negative Exponential, Logarithm, Square-Root, Power Utility Functions
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.6 No.2,
May
12,
2016
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-to-day is driven by the ratio of the risk neutral probability and the probability of rising to falling.