# Upper Bounds for Ruin Probability in a Controlled Risk Process under Rates of Interest with Homogenous Markov Chains

*Phung Quang* ()

*Journal of Statistical and Econometric Methods*, 2017, vol. 6, issue 3, 4

**Abstract:**
This paper explores recursive and integral equations for ruin probability of aÂ controlled risk process under rates of interest with homogenous Markov chains.Â We assume that claim and rates of interest are homogenous Markov chains, take aÂ countable number of non â€“ negative values. Generalized Lundberg inequalities forÂ ruin probability of this process are derived via a recursive technique. RecursiveÂ equations for finite time ruin probability and an integral equation for ultimate ruinÂ probability are presented, from which corresponding probability inequalities andÂ upper bounds are obtained. An illustrative numerical example is discussed.Mathematics Subject Classification: 62P05, 60G40, 12E05Keywords: ruin probability, homogenous Markov chain, controlled risk process

**Date:** 2017

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