A martingale argument is used to derive the generating function of the number of i.i.d. experiments it takes to observe a given string of outcomes for the first time. Then, a more general problem can be studied: How many trials does it take to observe a member of a finite set of strings for the...

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...

We consider a Markovian regime switching insurance risk model (also called Markov-modulated risk model). The closed form solutions for the joint distribution of surplus before and after ruin when the initial surplus is zero or when the claim size distributions are phase-type distributed are...