Mean-Variance Investment and Risk Control Strategies -- A Time-Consistent Approach via A Forward Auxiliary Process

TL;DR

This paper develops a time-consistent mean-variance investment and risk control strategy for insurers using a forward auxiliary process, providing closed-form solutions and insights into market conditions affecting investment behavior.

Contribution

It introduces a novel time-consistent approach to the mean-variance problem using a forward auxiliary process, with explicit solutions and comparative analysis.

Findings

Optimal strategies involve short selling in negatively correlated markets.

Less risk-averse insurers tend to short sell more risky assets.

Closed-form solutions are derived for the new formulation.

Abstract

We consider an optimal investment and risk control problem for an insurer under the mean-variance (MV) criterion. By introducing a deterministic auxiliary process defined forward in time, we formulate an alternative time-consistent problem related to the original MV problem, and obtain the optimal strategy and the value function to the new problem in closed-form. We compare our formulation and optimal strategy to those under the precommitment and game-theoretic framework. Numerical studies show that, when the financial market is negatively correlated with the risk process, optimal investment may involve short selling the risky asset and, if that happens, a less risk averse insurer short sells more risky asset.