TY - JOUR
T1 - Ruin Probability in a Generalised Risk Process under Rates of Interest with Homogenous Markov Chains
AU - Phung Duy Quang
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 283
EP - 300
PY - 2018
DA - 2018/02
SN - 4
DO - http://doi.org/10.4208/eajam.051013.230614a
UR - https://global-sci.org/intro/article_detail/eajam/10837.html
KW - Integral equation, recursive equation, ruin probability, homogeneous Markov chain.
AB - <p style="text-align: justify;">This article explores recursive and integral equations for ruin probabilities
of generalised risk processes, under rates of interest with homogenous Markov chain
claims and homogenous Markov chain premiums. We assume that claim and premium
take a countable number of non-negative values. Generalised Lundberg inequalities for
the ruin probabilities of these processes are derived via a recursive technique. Recursive
equations for finite time ruin probabilities and an integral equation for the ultimate ruin
probability are presented, from which corresponding probability inequalities and upper
bounds are obtained. An illustrative numerical example is discussed.</p>