Robust optimal consumption, investment and reinsurance for recursive preferences

Paper: arXiv 2511.03031

Authors: Elizabeth Dadzie, Wilfried Kuissi-Kamdem, Marcel Ndengo

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using advanced FBSDEs and Epstein-Zin recursive utility under ambiguity aversion. However, it lacks empirical validation, relying solely on synthetic numerical experiments rather than backtests on real-world market or insurance data.

Research Flowchart

  flowchart TD
    A[Research Goal: Robust Consumption, Investment & Reinsurance Strategy under Model Ambiguity] --> B[Inputs: Cramér-Lundberg Surplus, Epstein-Zin Preferences & Alternative Measure Class]
    B --> C[Formulate Max-Min Utility Problem under Worst-Case Scenario]
    C --> D[Derive & Solve Coupled Forward-Backward Stochastic Differential Equations]
    D --> E[Analytical Outcomes: Closed-Form Solutions for Value Function & Optimal Policies]
    E --> F[Numerical Analysis & Findings: Risk Aversion/EIS Lower Consumption; Co-dependence of Investment & Reinsurance]