Optimal Investment Strategy under the CEV Model with Stochastic Interest Rate

Yong He,Peimin Chen

doi:10.1155/2020/7489174

Abstract

Interest rate is an important macrofactor that affects asset prices in the financial market. As the interest rate in the real market has the property of fluctuation, it might lead to a great bias in asset allocation if we only view the interest rate as a constant in portfolio management. In this paper, we mainly study an optimal investment strategy problem by employing a constant elasticity of variance (CEV) process and stochastic interest rate. The assets of investment for individuals are supposed to be composed of one risk-free asset and one risky asset. The interest rate for risk-free asset is assumed to follow the Cox–Ingersoll–Ross (CIR) process, and the price of risky asset follows the CEV process. The objective is to maximize the expected utility of terminal wealth. By applying the dual method, Legendre transformation, and asymptotic expansion approach, we successfully obtain an asymptotic solution for the optimal investment strategy under constant absolute risk aversion (CARA) utility function. In the end, some numerical examples are provided to support our theoretical results and to illustrate the effect of stochastic interest rates and some other model parameters on the optimal investment strategy.

Highlights

E advantage of the constant elasticity of variance (CEV) process covers that the volatility of such a model has correlation with risky asset prices and can explain volatility smile efficiently
The CEV process has been employed to pension plans and used to search optimal investment strategy under different utility functions
One of important reasons is that the CEV process combining with the stochastic interest rate will make it very difficult to obtain the analytic solution for the optimal investment strategy

Summary

Model Formulations

We consider a simple portfolio, which is just composed of two financial assets. Where μ is an expected instantaneous rate of return, σ is the instantaneous volatility, and θ is the elasticity parameter Both W1(t) and W2(t) in (2) are standard Brownian motions. Let V(t) denote the individual wealth at time t, π(t) be the proportion of the wealth invested in risky asset. En, the proportion of wealth invested in risk-free asset is 1 − π(t). E wealth process V(t) satisfies the following stochastic process:. A strategy π(t) is said to be admissible if the following conditions are satisfied:. E aim of individuals is to maximize the expected utility of terminal wealth in the finite horizon as follows: sup E[U(V(T))],. The constant absolute risk aversion (CARA) utility is considered and it has the expression as e− qx

Optimization Process

Asymptotic Solution

Numerical Analysis

Conclusion