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Gerber-Shiu analysis with two-sided acceptable levels. (English) Zbl 1364.91071
Summary: In this paper, insurer’s surplus process moved within upper and lower levels is analyzed. To this end, a truncated type of Gerber-Shiu function is proposed by further incorporating the minimum and the maximum surplus before ruin into the existing ones (e.g. [H. U. Gerber and E. S. W. Shiu, N. Am. Actuar. J. 2, No. 1, 48–78 (1998; Zbl 1081.60550); E. C. K. Cheung et al., Insur. Math. Econ. 46, No. 1, 117–126 (2010; Zbl 1231.91157)]). A key component in our analysis of this proposed Gerber-Shiu function is the so-called transition kernel. Explicit expressions of the transition function under two different risk models are obtained. These two models are both generalizations of the classical Poisson risk model: (i) the first model provides flexibility in the net premium rate which is dependent on the surplus (such as linear or step function); and (ii) the second model assumes that claims arrive according to a Markovian arrival process (MAP). Finally, we discuss some applications of the truncated Gerber-Shiu function with numerical examples under various scenarios.
91B30 Risk theory, insurance (MSC2010)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
Full Text: DOI
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