Robust Time-Consistent Portfolio Selection for an Investor under CEV Model with Inflation Influence

Peng Yang

doi:10.1155/2020/2359135

Abstract

A robust time-consistent optimal investment strategy selection problem under inflation influence is investigated in this article. The investor may invest his wealth in a financial market, with the aim of increasing wealth. The financial market includes one risk-free asset, one risky asset, and one inflation-indexed bond. The price process of the risky asset is governed by a constant elasticity of variance (CEV) model. The investor is ambiguity-averse; he doubts about the model setting under the original probability measure. To dispel this concern, he seeks a set of alternative probability measures, which are absolutely continuous to the original probability measure. The objective of the investor is to seek a time-consistent strategy so as to maximize his expected terminal wealth meanwhile minimizing his variance of the terminal wealth in the worst-case scenario. By using the stochastic optimal control technique, we derive closed-form solutions for the optimal time-consistent investment strategy, the probability scenario, and the value function. Finally, the influences of model parameters on the optimal investment strategy and utility loss function are examined through numerical experiments.

Highlights

Nowadays, portfolio selection is a very important research topic in mathematical finance
We assume that the investor is ambiguity-averse and worries about uncertainty in model setting. He seeks a set of alternative probability measures, which are absolutely continuous to the original probability measure. en, the new model setting is obtained under the new probability measure
We have investigated a robust time-consistent MV strategy selection under the inflation risk for an ambiguity-averse investor (AAI). e AAI doubts the model setting under the original probability measure

Summary

Introduction

Portfolio selection is a very important research topic in mathematical finance. Li et al [20] studied the time-consistent investment strategy selection problem for a DC pension under partial information and inflation influence. Bearing in mind the aforementioned state of the art, in this article, we will investigate the time-consistent investment strategy under the CEV model with inflation influence. The influences of model parameters on the optimal investment strategy and utility loss function are examined through numerical experiments. (iii) Closed-form solutions for the optimal time-consistent robust investment strategy, optimal probability scenario, and value function are derived. (iv) e influences of model parameters on the optimal time-consistent investment strategy and utility loss function are systematically examined through numerical experiments.

Model Setup

Problem Formulation

Conclusions