Optimal (Re)Insurance Design: Ambiguity, Belief Heterogeneity, and Loss Aversion

最优（再）保险设计：模糊性、信念异质性和损失厌恶

• 批准号: RGPIN-2018-03961
• 负责人: Ghossoub, Mario
• 金额: $ 1.31万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=712185
• 关键词: Optimal; Re; Insurance; Design; Ambiguity

Financial crises have demonstrated the need for resilient financial and insurance markets. A key consideration in insurance markets is then the design of robust insurance contracts. Indeed, the theory of optimal insurance design is one of the cornerstones of actuarial science, and the question of what insurance contract is optimal from an insurance buyer's perspective lies at its core. A rigorous treatment of this question requires a mathematical formulation of an optimality criterion. The classical theory builds upon the foundations laid out by Arrow (1971) and is rooted in the classical model of choice under uncertainty, i.e. Expected-Utility Theory (EUT): an insurance seeker is a risk-averse EU-maximizing decision-maker (DM) facing an insurable loss represented by a random variable on a given probability space. In this case, classical Bayesian optimization methods can be used to show the optimality of a linear deductible contract. These foundational results have been extended in several directions while maintaining EUT's assumption that individuals are fully rational and know precisely the likelihoods associated with any decision-making situation. However, there is substantial empirical evidence that DMs are not rational in the sense of EUT and that the classical insurance model is too limiting. For instance, there are situations of ambiguity (model uncertainty) in which DMs are not able to fully assess the probabilistic environment involved, as well as situations where DMs differ from insurers in their assessment of likelihoods. Insurance of emerging risks is a prime example. It is critically important to construct more realistic models of DM behaviour in problems of optimal insurance design so as to align theoretical predictions with reality, suitably inform policy-making and insurance market regulation, and guide actuarial practice and efficient contract design. This is the long-term goal of the research program proposed herein, and a core component of my previous research has focused on advancing this effort. The proposed research program will continue on this path by building upon my previous work and incorporating belief heterogeneity, ambiguity aversion, and loss aversion in optimal insurance design. On a technical level, this research will present serious mathematical challenges arising from the inapplicability of Bayesian optimization and/or classical measure-theoretic methods in a setting of ambiguity and/or loss aversion. The optimal insurance design problems will be formulated as non-convex optimization problems involving non-additive probability measures and Choquet integration. Novel techniques are needed based on non-additive measure theory, and the research proposed herein will leverage my previous work to accomplish this. Student training will be embedded in this research program at every stage, as exhaustively described in my research proposal.

金融危机表明，需要有弹性的金融和保险市场。因此，保险市场的一个关键考虑因素是设计健全的保险合同。事实上，最优保险设计理论是精算科学的基石之一，从保险购买者的角度来看，什么样的保险合同是最优的问题是其核心。对这个问题的严格处理需要一个最优性准则的数学公式。经典理论建立在阿罗（1971）奠定的基础之上，植根于不确定性下的经典选择模型，即期望效用理论（EUT）：寻求保险的人是一个风险厌恶的欧盟最大化决策者（DM），面对由给定概率空间上的随机变量表示的可保险损失。在这种情况下，经典的贝叶斯优化方法可以用来证明线性可抵扣契约的最优性。