[论文解读] Optimal investment of participating contracts under VaR-Regulation

Thai Nguyen, Mitja Stadje|arXiv (Cornell University)|May 23, 2018

Insurance, Mortality, Demography, Risk Management被引用 1

一句话总结

本文在包含不可对冲死亡风险的完整金融市场上，采用鞅方法研究了在风险价值（VaR）监管下参与型终身保险合同的最优投资策略。研究发现，VaR约束导致投资行为更加审慎，相较于无监管情形，显著提升了保单持有人的效用，尤其在更严格的监管或投资组合保险型规则下效果更明显。

ABSTRACT

This paper studies a Value-at-Risk (VaR)-regulated optimal portfolio problem of the equity holders of a participating life insurance contract. In a setting with unhedgeable mortality risk and complete financial market, the optimal solution is given explicitly for contracts with mortality risk using a martingale approach for constrained non-concave optimization problems. We show that regulatory VaR constraints for participating insurance contracts lead to more prudent investment than in the case of no regulation. This result is contrary to the situation where the insurer maximizes the utility of the total wealth of the company (without distinguishing between contributions of equity holders and policyholders), in which case a VaR constraint may induce the insurer to take excessive risks leading to higher losses than in the case of no regulation. Compared to the unregulated problem, the VaR-constrained strategy leads to a higher expected utility for the policyholders, highlighting the potential usefulness of a VaR-regulation in the context of insurance. The prudent investment behavior is more significant if a VaR-type regulation is replaced by a portfolio insurance (PI)-type regulation. Furthermore, a stricter regulation (a smaller allowed default probability in the VaR problem or a higher minimum guarantee level in the PI problem) enhances the benefit of the policyholder but deteriorates that of the insurer. For both types of regulation, the gains in terms of expected utility are greater for higher participation rates, while being smaller for higher bonus rates. We also extend our analysis to frameworks where dividend and premature death benefit payments are made at an intermediate time date.

研究动机与目标

• 探讨VaR监管如何影响参与型终身保险合同中权益持有人的最优投资决策。
• 比较VaR监管与无监管效用最大化的差异，特别是对风险承担激励的影响。
• 评估监管严格程度及合同设计（如参与率、红利率）对保单持有人与保险公司收益的影响。
• 将分析扩展至包含中期红利支付与提前身故赔付的合同。

提出的方法

• 采用鞅方法求解VaR监管下的约束性非凹优化问题。
• 在包含不可对冲死亡风险的完整金融市场上建模保险公司的投资组合。
• 运用随机控制技术，显式推导出在VaR约束下的最优投资策略。
• 将VaR约束解与无监管情形进行比较，重点关注风险敞口与效用结果。
• 将框架扩展至包含中期现金流（如红利、早期身故赔付）的情形。
• 分析监管严格程度的影响，包括VaR中的违约概率降低与投资组合保险中的最低保证水平提高。

实验结果

研究问题

• RQ1 VaR监管如何改变参与型保险合同中权益持有人的最优投资策略？
• RQ2 与无监管情形相比，VaR监管是否导致更审慎的投资行为？如果是，原因是什么？
• RQ3 监管约束如何影响保单持有人与保险公司的预期效用？
• RQ4 参与率与红利率如何影响VaR监管的有效性？
• RQ5 中期支付（红利、提前身故赔付）如何影响VaR约束下的最优策略？

主要发现

• 与财富效用最大化中典型的VaR风险激励效应相反，VaR监管导致的投资行为比无监管情形更加审慎。
• 与无监管情形相比，VaR约束策略显著提升了保单持有人的预期效用，凸显了此类监管的潜在优势。
• 更严格的VaR监管（允许的违约概率更低）或投资组合保险型监管（最低保证水平更高）可增强保单持有人的收益，但会恶化保险公司的结果。
• 监管效益在参与率较高时更为显著，而在红利率较高时则相对较小。
• 在包含中期现金流的情形下，最优策略仍可显式求解，表明该框架对现实合同特征具有良好的稳健性。