Robust Optimal Reinsurance, Investment,and Surplus Allocation for Epstein-Zin Preferences

TL;DR

This paper derives explicit robust strategies for reinsurance, investment, and surplus distribution for insurers with Epstein-Zin preferences in incomplete markets, considering stochastic asset dynamics.

Contribution

It provides the first explicit solutions for robust reinsurance, investment, and consumption strategies under Epstein-Zin preferences with stochastic market parameters.

Findings

Explicit solutions for optimal strategies are derived and verified.

Robust solutions outperform non-robust ones in economic intuition.

Campbell-Shiller approximation accuracy is assessed.

Abstract

In this paper, we investigate the robust optimal reinsurance,investment,and internal surplus distribution (i.e., consumption) problem for an insurer with Epstein-Zin recursive preferences in an incomplete market. It is assumed that the insurer can allocate wealth to a financial market consisting of a risk-free asset and a risky asset, where the price process of the risky asset follows a diffusion process with a stochastic drift rate governed by an Ornstein-Uhlenbeck (O-U) process. For both the unit and non-unit elasticity of intertemporal substitution (EIS) cases, by applying the classical dynamic programming approach, we derive explicit solutions for the optimal robust reinsurance, investment,and consumption strategies and also verify that the obtained solutions indeed solve the optimal control problem. Furthermore, we compare the robust solutions with their non-robust counterparts, and the comparative results shown in the figures are consistent with economic intuition. Finally, we contrast the exact solutions with the Campbell-Shiller approximation and assess the accuracy of the approximation method.