Robust optimal consumption, investment and reinsurance for recursive preferences

TL;DR

This paper develops a comprehensive framework for insurers to optimize consumption, investment, and reinsurance strategies under model uncertainty and ambiguity aversion, providing explicit solutions and analyzing parameter effects.

Contribution

It introduces a novel approach using coupled FBSDEs to derive closed-form solutions for robust strategies under Epstein-Zin preferences and model ambiguity.

Findings

Optimal consumption decreases with higher risk aversion and EIS.

Investment and reinsurance strategies are interdependent on market parameters.

Ambiguity aversion significantly impacts optimal policies.

Abstract

This paper investigates a robust optimal consumption, investment, and reinsurance problem for an insurer with Epstein-Zin recursive preferences operating under model uncertainty. The insurer's surplus follows the diffusion approximation of the Cram\'er-Lundberg model, and the insurer can purchase proportional reinsurance. Model ambiguity is characterised by a class of equivalent probability measures, and the insurer, being ambiguity-averse, aims to maximise utility under the worst-case scenario. By solving the associated coupled forward-backward stochastic differential equation (FBSDE), we derive closed-form solutions for the optimal strategies and the value function. Our analysis reveals how ambiguity aversion, risk aversion, and the elasticity of intertemporal substitution (EIS) influence the optimal policies. Numerical experiments illustrate the effects of key parameters, showing that optimal consumption decreases with higher risk aversion and EIS, while investment and reinsurance strategies are co-dependent on both financial and insurance market parameters, even without correlation. This study provides a comprehensive framework for insurers to manage capital allocation and risk transfer under deep uncertainty.