Mean-variance portfolio selection and variance hedging with random coefficients: closed-loop equilibrium strategy

TL;DR

This paper derives explicit closed-loop equilibrium strategies for dynamic mean-variance portfolio selection and variance hedging problems with random coefficients in a non-Markovian framework, revealing new insights about their dependence on initial wealth.

Contribution

It introduces a unified approach to obtain explicit closed-loop equilibrium strategies for these problems under non-Markovian conditions, including cases with constant risk aversion and random risk-free rates.

Findings

Equilibrium strategies can depend on initial wealth when the risk-free rate is random.

Closed-loop and open-loop equilibrium strategies coincide if the risk-free rate is deterministic.

Explicit solutions are obtained for the first time in this non-Markovian setting.

Abstract

In this paper, both dynamic mean-variance portfolio selection problems and dynamic variance hedging problems are discussed under non-Markovian framework. Explicit closed-loop equilibrium strategies of these problems are respectively obtained via a unified approach for the first time. Several new interesting facts arise in mean-variance problems with constant risk aversion. For example, it is shown that equilibrium strategies are still allowed to rely on initial wealth as long as risk-free return rate is random. In addition, the closed-loop equilibrium strategy and open-loop equilibrium strategy have the same connection with initial wealth in non-Markovian setting, and they happen to equal to each other if only risk-free return rate is deterministic.