Insurance linked to financial markets: theory & applications

目前的金融环境，低利率，有时是负利率，加上政治不确定性增加，对保险公司和提供保险类合同的公司构成了巨大的挑战。特别是，传统的人寿保险或养老金产品在低利率环境下不再提供有吸引力的回报。这大大增加了未来养老金的成本，并鼓励保险客户取消保险或利用保险业以外的其他投资机会，这意味着我们的社会系统，特别是保险公司面临巨大困难。为了寻求更有吸引力的回报，保险公司推出了其回报取决于金融市场的产品，从而可以从这些市场获得有吸引力的投资机会。这类产品估值的理论基础仍然缺乏，突出了对这些产品估值的基本理解的发展需要。这是迈向有效风险管理的关键一步。在这个项目中，我们缩小了这一差距：我们的目标是一个基本的估值定理以及线性和非线性估值规则，重点是仿射半鞅驱动的模型。

The current financial environment with low and sometimes negative interest rates combined with increasing political uncertainty poses an immense challenge for insurance companies and companies providing insurance-like contracts. In particular, classical life insurances or pension products do no longer offer attractive pay-offs in low interest rate environment. This dramatically raises the costs for future pensions and encourages insurance customers to cancel insurances or take up other investment opportunities outside the insurance industry, implying large difficulties for our social systems and for the insurers in particular. Seeking for more attractive payoffs, insurance companies introduced products whose payoffs depend on the financial market, allowing to reach attractive investment opportunities from these markets. A theoretical foundation for the valuation of such products is still lacking, highlighting the need for the development of fundamental understanding of the valuation of these products. This is a crucial step towards efficient risk management. In this project we close this gap: we target at a fundamental valuation theorem together with linear and non-linear valuation rules with a focus on models driven by affine semimartingales.