An analysis of the interaction of contracts in a heterogeneous life insurance portfolio

An analysis of the interaction of contracts in a heterogeneous life insurance portfolio

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Speaker(s): Jonas Eckert, Stefan Graf, Alexander Kling (ifa Ulm)

Because of the long-term nature of insurance policies, the current low interest rate environment, and market based solvency capital requirements (e.g. under Solvency II), the fair valuation of insurance contracts becomes very important. Fair valuation is often discussed from the viewpoint of a portfolio of homogenous policies. In practice, however, insurance portfolios are heterogeneous. As an example, a typical German life insurance portfolio consists of policies with an annual return guarantee between 0,9% p.a. and 4% p.a.. These contracts are not independent, because they are invested in one common pool of assets and share reserves as well as the risk of default of the insurance company.

The work presents a method that allows for an analysis of these effects by measuring, whether one contract benefits from or subsidizes other contracts. For this, it introduces the concept of a collective bonus or collective malus, resp. The collective bonus or malus shows how much one contract benefits from or subsidizes, resp., the others. The work uses the theoretical concept and apply it to several examples from the existing literature and practice.

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