OPTIMAL INVESTMENT STRATEGY FOR AN INVESTOR WITH ORNSTEIN-UHLENBECK AND CONSTANT ELASTICITY OF VARIANCE (CEV) MODELS UNDER CORRELATING AND NON-CORRELATING BROWNIAN MOTION

Abstract

This paper is intended to determine the optimal investment strategy of an investor operating in the financial market where the interest rate of the risk-free asset is governed by a stochastic model and the risky asset is assumed to follow constant elasticity of variance model, in particular we examine the event where the Brownian motions correlates and does not correlate. The main objective of the paper is to obtain an optimal investment policy for an investor who faces power utility preference and investigate the deviations which occur when the Brownian motions correlate and do not correlate. The optimal investment strategy for the value function is defined as G(V,t;T)=〖Max〗_(π(t)) E[U(V)] subject to: dV(t)={(μ-r(t))π(t)+r(t)V(t)}dt+ bS^γ (t)π(t)dZ_1 (t) was constructed where r(t) is the risk free rate, π(t) is the amount invested in risky asset, dZ_1 (t) is the increase in the Wiener process, (μ,b) is the expected return and volatility of the stock market respectively and V is the utility preference and consequently applying Hamilton-Jacobi-Bellman equation and maximum principle technique to solve the power utility optimal investment strategy problem for an investor under constant elasticity of variance, we obtained a closed form solution π^*=[((μ-r))/(cb^2 S^2γ )+((1-c))/c]V to the optimal investment strategies. This result suggests that the amount invested in risky assets is proportional to total utility amount of money available for investment.