Compound Binomial Model with Batch Markovian Arrival Process

A compound binomial model with batch Markovian arrival process was studied, and the specific definitions are introduced. We discussed the problem of ruin probabilities. Specially, the recursion formulas of the conditional finite-time ruin probability are obtained and the numerical algorithm of the conditional finite-time nonruin probability is proposed. We also discuss research on the compound binomial model with batch Markovian arrival process and threshold dividend. Recursion formulas of the Gerber–Shiu function and the first discounted dividend value are provided, and the expressions of the total discounted dividend value are obtained and proved. At the last part, some numerical illustrations were presented.

Ruin problems in Markov-modulated risk models

Chen et al. (2014), studied a discrete semi-Markov risk model that covers existing risk models such as the compound binomial model and the compound Markov binomial model. We consider their model and build numerical algorithms that provide approximations to the probability of ultimate ruin and the probability and severity of ruin in a continuous time two-state Markov-modulated risk model. We then study the finite time ruin probability for a discrete m-state model and show how we can approximate the density of the time of ruin in a continuous time Markov-modulated model with more than two states.