Ruin problems in Markov-modulated risk models

Abstract

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.

Asymptotics and Approximations of Ruin Probabilities for Multivariate Risk Processes in a Markovian Environment

“…Markov-modulated risk models have been intensively studied (see e.g. Asmussen 1989, Reinhard 1984, Dickson & Qazvini 2018. The common basic idea is that the claim arrivals and claim amounts are influenced by an external environment process.…”