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

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  • Phung Duy Quang

Abstract

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

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  • Phung Duy Quang, 2017. "Upper Bounds for Ruin Probability in a Controlled Risk Process under Rates of Interest with Homogenous Markov Chains," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(3), pages 1-4.
    • Handle: RePEc:spt:stecon:v:6:y:2017:i:3:f:6_3_4
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    References listed on IDEAS

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    1. Cai, Jun & Dickson, David C.M., 2004. "Ruin probabilities with a Markov chain interest model," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 513-525, December.
    2. Promislow, S. David, 1991. "The probability of ruin in a process with dependent increments," Insurance: Mathematics and Economics, Elsevier, vol. 10(2), pages 99-107, July.
    3. Diasparra, Maikol & Romera, Rosario, 2009. "Inequalities for the ruin probability in a controlled discrete-time risk process," DES - Working Papers. Statistics and Econometrics. WS ws093513, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Sundt, Bjorn & Teugels, Jozef L., 1995. "Ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 7-22, April.
    5. Sundt, Bjorn & Teugels, Jozef L., 1997. "The adjustment function in ruin estimates under interest force," Insurance: Mathematics and Economics, Elsevier, vol. 19(2), pages 85-94, April.
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