Mean-variance-utility portfolio selection with time and state dependent risk aversion

TL;DR

This paper introduces a novel portfolio selection model where risk aversion varies with wealth and time, solved via game theory, revealing strategies that depend on wealth, income, and consumption preferences.

Contribution

It presents a new mean-variance-utility portfolio model incorporating dynamic risk aversion influenced by wealth and time, with analytical equilibrium solutions.

Findings

Optimal investment depends on investor's wealth and income balance.

Continuous consumption strategy aligns with investor's preferences.

Model's solutions are consistent with real-world investment behaviors.

Abstract

Under mean-variance-utility framework, we propose a new portfolio selection model, which allows wealth and time both have influences on risk aversion in the process of investment. We solved the model under a game theoretic framework and analytically derived the equilibrium investment (consumption) policy. The results conform with the facts that optimal investment strategy heavily depends on the investor's wealth and future income-consumption balance as well as the continuous optimally consumption process is highly dependent on the consumption preference of the investor.