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

Abstract EN

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.