Equilibrium reinsurance and investment strategies for insurers with random risk aversion under Heston's SV model

TL;DR

This paper develops a model for insurers to optimize reinsurance and investment strategies considering random risk aversion and stochastic volatility, providing semi-analytical solutions and numerical insights.

Contribution

It introduces a novel framework combining stochastic volatility, random risk aversion, and game theory to derive equilibrium strategies for insurers.

Findings

Semi-analytical formulas for strategies and value functions are derived.

Numerical experiments illustrate strategy characteristics under various conditions.

The model captures the impact of stochastic volatility on insurer decision-making.

Abstract

This study employs expected certainty equivalents to explore the reinsurance and investment issue pertaining to an insurer that aims to maximize the expected utility while being subject to random risk aversion. The insurer's surplus process is modeled approximately by a drifted Brownian motion, and the financial market is comprised of a risk-free asset and a risky asset with its price depicted by Heston's stochastic volatility (SV) model. Within a game theory framework, a strict verification theorem is formulated to delineate the equilibrium reinsurance and investment strategies as well as the corresponding value function. Furthermore, through solving the pseudo Hamilton-Jacobi-Bellman (HJB) system, semi-analytical formulations for the equilibrium reinsurance and investment strategies and the associated value function are obtained under the exponential utility. Additionally, several numerical experiments are carried out to demonstrate the characteristics of the equilibrium reinsurance and investment strategies.