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Zbl 1168.91421
Zhu, Jinxia; Yang, Hailiang
On differentiability of ruin functions under Markov-modulated models. (English)
[J] Stochastic Processes Appl. 119, No. 5, 1673-1695 (2009). ISSN 0304-4149

Summary: This paper analyzes the continuity and differentiability of several classes of ruin functions under Markov-modulated insurance risk models with a barrier and threshold dividend strategy, respectively. Many ruin related functions in the literature, such as the expectation and the Laplace transform of the Gerber-Shiu discounted penalty function at ruin, of the total discounted dividends until ruin, and of the time-integrated discounted penalty and/or reward function of the risk process, etc, are special cases of the functions considered in this paper. Continuity and differentiability of these functions in the corresponding dual models are also studied.

MSC 2000:: *91B30 Risk theory etc.

Keywords: ruin function; Markov-modulated model; dual model; strong Markov property; differentiability; Gerber-Shiu function

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