Analysis of some ruin-related quantities in a Markov-modulated risk model. Issue 3 (2nd July 2016)

• Record Type: Journal Article
• Authors: Li, Jingchao; Dickson, David C. M.; Li, Shuanming
• Is Part Of: Stochastic models. Volume 32:Issue 3(2016)
• Page Start: 351
• Page End: 365
• Publication Date: 2016-07-02
• Subjects: Duration in a certain state -- first hitting time -- Markov-modulated risk model -- matrix scale function -- number of claims and aggregate claims in a certain state; 91B30 -- 97M30; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/15326349.2015.1121399
• Languages: English
• ISSNs: 1532-6349

Abstract

ABSTRACT: In this paper, we study the joint Laplace transform and probability generating function of some random quantities that occur in each environment state by the time of ruin in a Markov-modulated risk process. These quantities include the duration spent in each state, the number of claims and the aggregate amount of claims that occurred in each state by the time of ruin. Explicit formulae for the joint transforms, given the initial surplus, and the initial and terminal environment states, are expressed in terms of a matrix version of the scale function. Moments and covariances of these ruin-related quantities are obtained and numerical illustrations are presented. The joint transform of the duration spent in each state, the number of claims, and the aggregate amount of claims that occurred in each state by the time the surplus attains a certain level are also investigated.