ABSTRACT In a participating endowment contract, the special loss compensation and profit sharing mechanism leads to heterogeneous benchmarks to distinguish the gain and loss for the policyholder's and the insurance company's S-shaped utilities. Because of the intense competition among the insurance companies and the requirement of the regulators, the benefits of the policyholders should be considered. As such, choosing the weighted utility of the two counterparts as the optimization objective is a rational setting. This setting induces a non-HARA (hyperbolic absolute risk aversion) and non-concave objective utility whose exact concavity and convexity are unknown. The difficulties not only come from this highly non-concave optimization problem, but also exist in the implicit integration of the optimum when solving the expected utilities of the two counterparts. We originally design an identification method to establish two categories of concave envelopes to solve the optimization problem, and propose an innovative numerical integration by substitution technique to deal with the implicit integration problem. The numerical simulation results recognize the existence of Pareto improvement of the two counterparts, which shows that the utilities of the policyholder and the insurance company can be simultaneously improved by switching into the weighted objective and appropriately amending the contract.

中文翻译：

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分红养老合约的加权效用优化

摘要 在分红养老合同中，特殊的损失补偿和利润分享机制导致了异质基准来区分投保人和保险公司的S型公用事业的损益。由于保险公司之间的激烈竞争和监管机构的要求，应考虑保单持有人的利益。因此，选择两个对应物的加权效用作为优化目标是一个合理的设置。此设置会导致非 HARA（双曲线绝对风险厌恶）和非凹目标效用，其确切的凹度和凸度未知。困难不仅来自这个高度非凹的优化问题，但也存在于求解两个对应物的预期效用时的最优值的隐式积分。我们最初设计了一种识别方法来建立两类凹包络来解决优化问题，并提出了一种创新的替代技术数值积分来处理隐式积分问题。数值模拟结果承认了两个对应方的帕累托改进的存在，这表明投保人和保险公司的效用可以通过切换到加权目标和适当修改合同来同时提高。并提出了一种创新的替代技术数值积分来处理隐式积分问题。数值模拟结果承认了两个对应方的帕累托改进的存在，这表明投保人和保险公司的效用可以通过切换到加权目标并适当修改合同来同时提高。并提出了一种创新的替代技术数值积分来处理隐式积分问题。数值模拟结果承认了两个对应方的帕累托改进的存在，这表明投保人和保险公司的效用可以通过切换到加权目标和适当修改合同来同时提高。