稳健渐近保险-金融套利
Robust asymptotic insurance-finance arbitrage
摘要：
在大多数情况下，保险合同与金融市场挂钩，例如通过利率或与股票挂钩的保险产品。为了激励这些混合市场中的评估规则，Artzner等人（2022）引入了保险-金融套利的概念。在本文中，我们将模型的不确定性扩展他们的设置。为此，我们允许统计不确定性的基础动力学表示的一组先验$\mathscr{P}$。在这个框架内，我们引入了强大的渐近保险金融套利的概念，并描述了没有这样的策略的概念，${Q}\mathscr{P}$ -评价。这是一个非线性的两步评估，保证没有鲁棒渐近保险金融套利。此外，${Q}\mathscr{P}$ -评估占主导地位的所有两步评估，只要我们同意的先验集$\mathscr{P}$，这表明，这些两步评估不允许稳健的渐近保险融资套利。在此基础上，我们引入了一个不确定条件下的双随机投降和生存模型。在这种情况下，我们描述了条件依赖的Copula和说明如何使用的${Q}\mathscr{P}$评估混合保险产品的定价。
英文摘要：
In most cases, insurance contracts are linked to the financial markets, such as through interest rates or equity-linked insurance products. To motivate an evaluation rule in these hybrid markets, Artzner et al. (2022) introduced the notion of insurance-finance arbitrage. In this paper we extend their setting by incorporating model uncertainty. To this end, we allow statistical uncertainty in the underlying dynamics to be represented by a set of priors $\mathscr{P}$. Within this framework we introduce the notion of robust asymptotic insurance-finance arbitrage and characterize the absence of such strategies in terms of the concept of ${Q}\mathscr{P}$-evaluations. This is a nonlinear two-step evaluation which guarantees no robust asymptotic insurance-finance arbitrage. Moreover, the ${Q}\mathscr{P}$-evaluation dominates all two-step evaluations as long as we agree on the set of priors $\mathscr{P}$ which shows that those two-step evaluations do not allow for robust asymptotic insurance-finance arbitrages. Furthermore, we introduce a doubly stochastic model under uncertainty for surrender and survival. In this setting, we describe conditional dependence by means of copulas and illustrate how the ${Q}\mathscr{P}$-evaluation can be used for the pricing of hybrid insurance products.
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