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Risk-minimizing portfolio selection for insurance payment processes under a Markov-modulated model. (English) Zbl 1281.90091

Summary: This paper extends the model of M. Riesner [Insur. Math. Econ. 38, No. 3, 599–608 (2006; Zbl 1168.91419)] to a Markov modulated Lévy process. The parameters of the Lévy process switch over time according to the different states of an economy, which is described by a finite-state continuous time Markov chain. Employing the local risk minimization method, we find an optimal hedging strategy for a general payment process. Finally, we give an example for single unit-linked insurance contracts with guarantee to display the specific locally risk-minimizing hedging strategy.

MSC:

90C90 Applications of mathematical programming
91B30 Risk theory, insurance (MSC2010)
60J60 Diffusion processes
60G51 Processes with independent increments; Lévy processes

Citations:

Zbl 1168.91419
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