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Probability of Ruin under Inflationary Conditions or under Experience Rating

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  • Taylor, G. C.

Abstract

The effect of inflation of premium income and claims size distribution, but not of free reserves, on the probability of ruin of an insurer is studied.An interesting similarity between this problem and the ruin problem in an experience-rated scheme is exhibited. This similarity allows the deduction of parallel results for the two problems in later sections.It is shown that the probability of ruin is always increased when the (constant) inflation rate is increased.The distribution of aggregate claims under inflationary conditions is described and used to calculate an upper bound on the ruin probability. Some numerical examples show that this bound is not always sharp enough to be practically useful. It is also shown, however, that this bound can be used to construct an approximation of the effect of inflation on ruin probability.It is shown that if inflation occurs at a constant rate, then ruin is certain, irrespective of the smallness of that rate and of the largeness of initial free reserves and the safety margin in the premium. The corresponding result for experiencerated schemes is that a practical and “intuitively reasonable” experience-rating scheme leads eventually to certain ruin.Finally, a simple modification of the techniques of the paper is made in order to bring investment income into account.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:astinb:v:10:y:1979:i:02:p:149-162_00
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    Cited by:

    1. Wang, Guojing & Wu, Rong, 2001. "Distributions for the risk process with a stochastic return on investments," Stochastic Processes and their Applications, Elsevier, vol. 95(2), pages 329-341, October.
    2. Franck Adékambi & Kokou Essiomle, 2021. "Asymptotic Tail Probability of the Discounted Aggregate Claims under Homogeneous, Non-Homogeneous and Mixed Poisson Risk Model," Risks, MDPI, vol. 9(7), pages 1-22, June.
    3. Huynh, Mirabelle & Landriault, David & Shi, Tianxiang & Willmot, Gordon E., 2015. "On a risk model with claim investigation," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 37-45.
    4. Jang, Jiwook, 2007. "Jump diffusion processes and their applications in insurance and finance," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 62-70, July.
    5. Leveille, Ghislain & Garrido, Jose, 2001. "Moments of compound renewal sums with discounted claims," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 217-231, April.
    6. Ren, Jiandong, 2012. "A multivariate aggregate loss model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 402-408.
    7. 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.
    8. Jang, Ji-Wook & Krvavych, Yuriy, 2004. "Arbitrage-free premium calculation for extreme losses using the shot noise process and the Esscher transform," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 97-111, August.
    9. Woo, Jae-Kyung & Cheung, Eric C.K., 2013. "A note on discounted compound renewal sums under dependency," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 170-179.
    10. Shuanming Li & Yi Lu, 2018. "On the Moments and the Distribution of Aggregate Discounted Claims in a Markovian Environment," Risks, MDPI, vol. 6(2), pages 1-16, May.
    11. Adekambi Franck & Mamane Salha, 2012. "Health Care Insurance Pricing Using Alternating Renewal Processes," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 7(1), pages 1-14, December.
    12. Eric C.K. Cheung & Haibo Liu & Jae-Kyung Woo, 2015. "On the Joint Analysis of the Total Discounted Payments to Policyholders and Shareholders: Dividend Barrier Strategy," Risks, MDPI, vol. 3(4), pages 1-24, November.

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