Volume 4, Issue 3
Ruin Probability in a Generalised Risk Process under Rates of Interest with Homogenous Markov Chains

Phung Duy Quang

East Asian J. Appl. Math., 4 (2014), pp. 283-300.

Published online: 2018-02

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  • Abstract

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.

  • Keywords

Integral equation recursive equation ruin probability homogeneous Markov chain

  • AMS Subject Headings

62P05 60G40 12E05

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-4-283, author = {Phung Duy Quang}, title = {Ruin Probability in a Generalised Risk Process under Rates of Interest with Homogenous Markov Chains}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {4}, number = {3}, pages = {283--300}, abstract = {

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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.051013.230614a}, url = {http://global-sci.org/intro/article_detail/eajam/10837.html} }
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 KW - recursive equation KW - ruin probability KW - homogeneous Markov chain AB -

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.

Phung Duy Quang. (1970). Ruin Probability in a Generalised Risk Process under Rates of Interest with Homogenous Markov Chains. East Asian Journal on Applied Mathematics. 4 (3). 283-300. doi:10.4208/eajam.051013.230614a
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