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Hedging of unit-linked life insurance contracts with unobservable mortality hazard rate via local risk-minimization. (English) Zbl 1308.91077

Summary: In this paper we investigate the local risk-minimization approach for a combined financial-insurance model where there are restrictions on the information available to the insurance company. In particular we assume that, at any time, the insurance company may observe the number of deaths from a specific portfolio of insured individuals but not the mortality hazard rate. We consider a financial market driven by a general semimartingale and we aim to hedge unit-linked life insurance contracts via the local risk-minimization approach under partial information. The Föllmer-Schweizer decomposition of the insurance claim and explicit formulas for the optimal strategy for pure endowment and term insurance contracts are provided in terms of the projection of the survival process on the information flow. Moreover, in a Markovian framework, this leads to a filtering problem with point process observations.

MSC:

91B30 Risk theory, insurance (MSC2010)
60J25 Continuous-time Markov processes on general state spaces
60G35 Signal detection and filtering (aspects of stochastic processes)
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
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