AI 中文总结
研究有限状态空间上非马尔可夫标记点过程在转移率不确定下的鲁棒效用最大化问题，通过证明鞅最优性原理等，建立保险合同预期储备的存在唯一性，还得出了有幂效用偏好的鲁棒消费 - 保险问题的显式解。
AI 中文摘要
我们考虑在有限状态空间上非马尔可夫标记点过程类中，有界累积转移率不确定性下的一个新型鲁棒效用最大化问题。效用在可允许控制类上最大化，而自然从由路径依赖上下界限制的可允许、路径依赖累积转移率类中选择最坏情况的生物特征场景。我们证明了一个鞅最优性原理以及一个非标准最坏情况倒向随机微分方程的新存在唯一性结果，这使我们能够建立具有储备依赖支付的人寿和健康保险合同最坏情况和最佳情况预期储备的存在唯一性。最后，我们找到了具有幂效用偏好的新型鲁棒消费 - 保险问题的显式解。
英文摘要
We consider a novel robust utility maximisation problem under bounded cumulative transition rate uncertainty within the class of non-Markovian marked point processes on a finite state-space. Utility is maximised over the class of admissible controls, while Nature chooses a worst-case biometric scenario from the class of admissible, path-dependent cumulative transition rates restricted by path-dependent upper and lower bounds. We prove a martingale optimality principle and a novel existence and uniqueness result for a non-standard worst-case backwards stochastic differential equation, which allows us to establish existence and uniqueness of worst-case and best-case prospective reserves of life and health insurance contracts with reserve-dependent payments. Finally, we find an explicit solution of a novel robust consumption-insurance problem with power utility preferences.
