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The Asymptotic Ruin Problem in Health Care Insurance with Interest

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  • Adekambi Franck

    (Department of School of Statistics and Actuarial Science, University of the Witwatersrand, Private Bag 3, Johannesburg, Gauteng 2050, South Africa)

Abstract

This article considers the same model as Ramsay (“The Asymptotic Ruin Problem When the Healthy and Sickness Periods Form an Alternating Renewal Process.” Insurance: Mathematics and Economics 3:139–43) modified by the inclusion of the interest rate. Exponential type upper bounds for the ultimate ruin probability are derived by martingale and recursive techniques. To illustrate the results, we consider the cases where the length of sickness period and that of healthy period follow Erlang distribution. We then compare numerically the upper bound derived by each technique.

Suggested Citation

  • Adekambi Franck, 2013. "The Asymptotic Ruin Problem in Health Care Insurance with Interest," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 7(2), pages 143-162, July.
    • Handle: RePEc:bpj:apjrin:v:7:y:2013:i:2:p:143-162:n:6
    DOI: 10.1515/apjri-2013-0003
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    References listed on IDEAS

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    1. Powers, Michael R., 1995. "A theory of risk, return and solvency," Insurance: Mathematics and Economics, Elsevier, vol. 17(2), pages 101-118, October.
    2. Yuen, Kam C. & Wang, Guojing & Wu, Rong, 2006. "On the renewal risk process with stochastic interest," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1496-1510, October.
    3. Taylor, G. C., 1979. "Probability of Ruin under Inflationary Conditions or under Experience Rating," ASTIN Bulletin, Cambridge University Press, vol. 10(2), pages 149-162, March.
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