On differentiability of ruin functions under Markov-modulated models

Jinxia Zhu, Hailiang Yang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1673-1695
JournalStochastic Processes and their Applications
Publication statusPublished - 2009
Externally publishedYes


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