Behavioral Participating Insurance: Optimal Investment under Probability Distortion and Aspiration Constraints

2026-08-16

AI Summary

This study investigates optimal investment strategies for participating insurance under probability distortion and expectation constraints. Within an extended hope-fear framework, it employs quantile optimization, concavification techniques, and asymptotic analysis to elucidate the interaction between non-concave utility and probability weighting. The research derives closed-form optimal policies, revealing how probability distortion influences risk-taking behavior and characterizing regime-switching dynamics induced by regulatory thresholds. By providing explicit solutions and theoretical foundations for insurance asset allocation under dual behavioral preferences and solvency constraints, this work effectively bridges a critical gap at the intersection of behavioral finance and actuarial science.

Abstract

We study optimal investment for insurers managing participating (profit-sharing) contracts under probability distortion and probability benchmark (aspiration) constraints. The problem combines three theoretical complexities: (i) nonconcave effective utilities induced by embedded guarantees and surplus-sharing rules, (ii) probability weighting capturing behavioral aspects of long-horizon decisions, and (iii) aspiration-type constraints formalizing solvency requirements. Using quantile formulations and concavification techniques, we derive explicit closed-form solutions for optimal terminal wealth and trading strategies in both complete and incomplete Black-Scholes markets. Our utility class accommodates the piecewise hyperbolic absolute risk aversion (PHARA) family and covers nonconcavities arising naturally in insurance contexts. The framework reveals how probability distortion weakens lock-in behavior and induces time inconsistency: under inverse S-shaped distortions, insurers overestimate upside probabilities and increase risky investment relative to undistorted benchmarks. Asymptotic analysis and numerical illustrations demonstrate regime switches in optimal policies driven by regulatory thresholds and capital constraints. Our results extend the hope-fear-aspirations framework of He and Zhou (2016) and provide practical insights for managing insurance balance sheets under behavioral preferences and solvency constraints.

Problem

• Participating Insurance
• Optimal Investment
• Probability Distortion
• Aspiration Constraints
• Nonconcave Utility

Innovation

• Probability Distortion
• Nonconcave Utility
• Closed-form Solutions
• Aspiration Constraints
• Quantile Formulation