AI 中文总结
该研究针对保险公司在概率扭曲和目标约束下的参与型合同最优投资问题，推导了完全与不完全 Black-Scholes 市场的闭式解，扩展了希望-恐惧-目标框架，为保险资产负债表管理提供了实用见解。
AI 中文摘要
我们研究保险公司在概率扭曲和概率基准（目标）约束下管理参与型（利润分享）合同的最优投资问题。该问题结合了三类理论复杂性：（i）内嵌担保和盈余分享规则诱导的非凹有效效用；（ii）捕捉长期决策行为方面的概率加权；（iii）形式化为偿付能力要求的目标型约束。利用分位数公式和凹化技术，我们在完全和不完全的 Black-Scholes 市场中推导了最优期末财富和交易策略的显式闭式解。我们的效用类别容纳了分段双曲绝对风险厌恶（PHARA）族，涵盖了保险环境中自然产生的非凹性。该框架揭示了概率扭曲如何削弱锁定行为并诱导时间不一致性：在反 S 形扭曲下，保险公司高估上行概率，相对于无扭曲基准增加风险投资。渐近分析和数值示例表明，最优政策存在由监管阈值和资本约束驱动的制度转换。我们的结果扩展了 He 和 Zhou（2016）的希望-恐惧-目标框架，为在行为偏好和偿付能力约束下管理保险资产负债表提供了实用见解。
英文摘要
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.
Comments38 pages, 9 figures
