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A characterization of progressively equivalent probability measures preserving the structure of a compound mixed renewal process

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  • Spyridon M. Tzaninis
  • Nikolaos D. Macheras

Abstract

Generalizing earlier works of Delbaen & Haezendonck [5] as well as of [18] and [16] for given compound mixed renewal process S under a probability measure P, we characterize all those probability measures Q on the domain of P such that Q and P are progressively equivalent and S remains a compound mixed renewal process under Q with improved properties. As a consequence, we prove that any compound mixed renewal process can be converted into a compound mixed Poisson process through a change of measures. Applications related to the ruin problem and to the computation of premium calculation principles in an insurance market without arbitrage opportunities are discussed in [26] and [27], respectively.

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  • Spyridon M. Tzaninis & Nikolaos D. Macheras, 2020. "A characterization of progressively equivalent probability measures preserving the structure of a compound mixed renewal process," Papers 2007.05289, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:2007.05289
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    References listed on IDEAS

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    1. Haslip, Gareth G. & Kaishev, Vladimir K., 2010. "Pricing of Reinsurance Contracts in the Presence of Catastrophe Bonds," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 307-329, May.
    2. Chi-Hsuan Chen & Jui-Pin Wang & Yih-Min Wu & Chung-Han Chan & Chien-Hsin Chang, 2013. "A study of earthquake inter-occurrence times distribution models in Taiwan," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 69(3), pages 1335-1350, December.
    3. Delbaen, F. & Haezendonck, J., 1989. "A martingale approach to premium calculation principles in an arbitrage free market," Insurance: Mathematics and Economics, Elsevier, vol. 8(4), pages 269-277, December.
    4. Boogaert, P. & De Waegenaere, A., 1990. "Simulation of ruin probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 95-99, September.
    5. Geman, Helyette & Yor, Marc, 1997. "Stochastic time changes in catastrophe option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 185-193, December.
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