Mean-Variance Optimization for Participating Life Insurance Contracts

TL;DR

This paper develops explicit formulas for optimal investment strategies in participating life insurance contracts within Black-Scholes markets, analyzing how equity holders adjust their portfolios in different economic states.

Contribution

It provides explicit solutions for optimal portfolio strategies in life insurance contracts and extends analysis to incomplete markets using HJB equations.

Findings

Equity holders increase risky asset investment in bad economic states.

Optimal strategies are explicitly derived in Black-Scholes models.

Numerical analysis illustrates dynamic investment behavior over time.

Abstract

This paper studies the equity holders' mean-variance optimal portfolio choice problem for (non-)protected participating life insurance contracts. We derive explicit formulas for the optimal terminal wealth and the optimal strategy in the multi-dimensional Black-Scholes model, showing the existence of all necessary parameters. In incomplete markets, we state Hamilton-Jacobi-Bellman equations for the value function. Moreover, we provide a numerical analysis of the Black-Scholes market. The equity holders on average increase their investment into the risky asset in bad economic states and decrease their investment over time.