Robust optimal consumption, investment and reinsurance for recursive preferences
Elizabeth Dadzie, Wilfried Kuissi-Kamdem, Marcel Ndengo
TL;DR
This work addresses robust optimization of consumption, investment, and proportional reinsurance for an insurer endowed with Epstein–Zin recursive utility under model uncertainty. It embeds a diffusion-approximation of the Cramér–Lundberg surplus into a two-asset market and a liability at horizon, solving a max–min problem via coupled forward–backward stochastic differential equations to obtain closed-form robust controls and the value function. The main contributions include explicit optimal strategies for consumption, investment, reinsurance, and worst-case distortion, along with a detailed analysis of how ambiguity aversion ($\Phi$), risk aversion ($\gamma$) and EIS ($\psi$) shape these policies, including their interdependence even when markets are uncorrelated. Numerical experiments illustrate the sensitivity of the robust policies to key parameters and demonstrate the co-dependence between financial and insurance decisions under deep uncertainty, providing a comprehensive framework for insurer risk transfer and capital allocation under misspecification.
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 Cramér-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.