Optimal Credit Investment and Risk Control for an Insurer with Regime-Switching

TL;DR

This paper develops a model for an insurer's optimal investment and risk management in a regime-switching environment with default contagion, providing strategies to maximize expected utility of terminal wealth.

Contribution

It introduces a novel framework combining regime-switching and default contagion for optimal insurer investment and risk control, with rigorous solution analysis.

Findings

Characterized optimal trading strategies for defaultable stocks and risk control.

Proved existence and uniqueness of solutions to the recursive HJB system.

Validated the optimal strategies through a verification theorem.

Abstract

This paper studies an optimal investment and risk control problem for an insurer with default contagion and regime-switching. The insurer in our model allocates his/her wealth across multi-name defaultable stocks and a riskless bond under regime-switching risk. Default events have an impact on the distress state of the surviving stocks in the portfolio. The aim of the insurer is to maximize the expected utility of the terminal wealth by selecting optimal investment and risk control strategies. We characterize the optimal trading strategy of defaultable stocks and risk control for the insurer. By developing a truncation technique, we analyze the existence and uniqueness of global (classical) solutions to the recursive HJB system. We prove the verification theorem based on the (classical) solutions of the recursive HJB system.