Insurance linked to financial markets: theory & applications

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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.