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The tax identity for Markov additive risk processes. (English) Zbl 1286.91062

This paper extends the tax identities of H. Albrecher and C. Hipp [Bl. DGVFM 28, No. 1, 13–28 (2007; Zbl 1119.62103)] to risk models driven by spectrally-negative Markov additive processes (MAP) and gives reasons for a wide generalization of related theory. After in-depth analysis concerning the tax identity for the Cramér-Lundberg process, the study focuses on the Sparre Andersen model with phase-type interarrival times. Then a presentation of basic notations and results concerning MAP is provided, together with several examples of risk processes that can be viewed as MAPs. In particular the taxed MAP-driven risk process is considered and investigated. The special case of a spectrally-negative MAP concludes the analysis, and some numerical examples are presented.

MSC:

91B30 Risk theory, insurance (MSC2010)
60G51 Processes with independent increments; Lévy processes
60J75 Jump processes (MSC2010)
60K37 Processes in random environments

Citations:

Zbl 1119.62103
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References:

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