On differentiability of ruin functions under Markov-modulated models

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Zhu, Jinxia²  Yang, Hailiang¹ 

[1] Univ Hong Kong, Dept Stat & Actuarial Sci, Hong Kong, Hong Kong, Peoples R China

[2] Univ New S Wales, Australian Sch Business, Sydney, NSW, Australia

关键词: Ruin function;    Markov-modulated model;    Dual model;    Strong Markov property;    Differentiability;    Gerber-Shiu function;   

DOI  :  10.1016/j.spa.2008.08.007

来源: Elsevier

【 摘 要 】

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. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free