SIAM Journal on Control and Optimization, Volume 58, Issue 2, Page 895-936, January 2020.
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 nonconcave 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; see [S. Basak and A. Shapiro, Rev. Financ. Stud., 14 (2001), pp. 371--405]. 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.

中文翻译：

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具有风险价值约束的非凹型最优投资：在人寿保险合同中的应用

SIAM控制与优化杂志，第58卷，第2期，第895-936页，2020年1月。
本文研究了参与人寿保险合同的权益持有人在风险价值（VaR）约束下的最优投资组合问题。在无法避免的死亡风险和完整的金融市场的环境中，使用using方法解决约束的非凹优化问题，从而明确给出了具有死亡风险的合同的最优解决方案。我们表明，与没有监管的情况相比，参与保险合同的监管VaR约束导致更为谨慎的投资。此结果与保险公司最大程度地利用公司总财富的使用情况（不区分股权持有人和保单持有人的出资）的情况相反，在这种情况下，VaR约束可能会导致保险人承担过多风险，从而导致更高的损失比没有监管的情况要多；参见[S. Basak和A. Shapiro，Financ牧师。Stud。，14（2001），371--405页。与不受监管的问题相比，受VaR约束的策略可为保单持有人带来更高的预期效用，突出了VaR法规在保险领域的潜在实用性。如果VaR型法规被证券投资保险（PI）型法规替代，则谨慎的投资行为将更为重要。此外，更严格的规定（VaR问题中允许的违约概率较小或PI问题中的最低担保水平较高）会增强保单持有人的利益，但会损害保险公司的利益。对于两种类型的监管，参与率越高，期望效用的收益就越大，而奖金率越高，收益的收益就越小。