IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2007.05289.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2007.05289
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Burnecki, Krzysztof & Giuricich, Mario Nicoló & Palmowski, Zbigniew, 2019. "Valuation of contingent convertible catastrophe bonds — The case for equity conversion," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 238-254.
    2. Sutapa Chaudhuri & Arumita Roy Chowdhury & Payel Das, 2018. "Implementation of Sugeno: ANFIS for forecasting the seismic moment of large earthquakes over Indo-Himalayan region," 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. 90(1), pages 391-405, January.
    3. Sumanta Pasari & Onkar Dikshit, 2014. "Three-parameter generalized exponential distribution in earthquake recurrence interval estimation," 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. 73(2), pages 639-656, September.
    4. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Martellini, Lionel, 2005. "Dynamic asset pricing theory with uncertain time-horizon," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1737-1764, October.
    5. J. Wang, 2016. "Reviews of seismicity around Taiwan: Weibull distribution," 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. 80(3), pages 1651-1668, February.
    6. Shah, Anand, 2016. "Pricing and Risk Mitigation Analysis of a Cyber Liability Insurance using Gaussian, t and Gumbel Copulas – A case for Cyber Risk Index," MPRA Paper 111968, University Library of Munich, Germany.
    7. Y. Esmaeelzade Aghdam & A. Neisy & A. Adl, 2024. "Simulating and Pricing CAT Bonds Using the Spectral Method Based on Chebyshev Basis," Computational Economics, Springer;Society for Computational Economics, vol. 63(1), pages 423-435, January.
    8. Perrakis, Stylianos & Boloorforoosh, Ali, 2013. "Valuing catastrophe derivatives under limited diversification: A stochastic dominance approach," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3157-3168.
    9. Iwaki, Hideki & Kijima, Masaaki & Morimoto, Yuji, 2001. "An economic premium principle in a multiperiod economy," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 325-339, June.
    10. Sukono & Hafizan Juahir & Riza Andrian Ibrahim & Moch Panji Agung Saputra & Yuyun Hidayat & Igif Gimin Prihanto, 2022. "Application of Compound Poisson Process in Pricing Catastrophe Bonds: A Systematic Literature Review," Mathematics, MDPI, vol. 10(15), pages 1-19, July.
    11. Wang, Shaun, 1996. "Ordering of risks under PH-transforms," Insurance: Mathematics and Economics, Elsevier, vol. 18(2), pages 109-114, July.
    12. Lev Eppelbaum, 2013. "Non-stochastic long-term prediction model for US tornado level," 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 2269-2278, December.
    13. Stephen J. Mildenhall, 2017. "Actuarial Geometry," Risks, MDPI, vol. 5(2), pages 1-44, June.
    14. Beer, Simone & Braun, Alexander & Marugg, Andrin, 2019. "Pricing industry loss warranties in a Lévy–Frailty framework," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 171-181.
    15. Francesca Biagini & Jan Widenmann, 2012. "Pricing Of Unemployment Insurance Products With Doubly Stochastic Markov Chains," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1-32.
    16. Pérez-Fructuoso, María José, 2017. "Tarificación de bonos sobre catástrofes (cat bonds) con desencadenantes de índices de pérdidas. Modelación mediante un proceso de Ornstein-Uhlenbeck || Pricing Loss Index Triggered Cat Bonds. An Ornst," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 24(1), pages 340-361, Diciembre.
    17. Muermann, Alexander, 2002. "Pricing catastrophe insurance derivatives," LSE Research Online Documents on Economics 24904, London School of Economics and Political Science, LSE Library.
    18. Møller, T., 2002. "On Valuation and Risk Management at the Interface of Insurance and Finance," British Actuarial Journal, Cambridge University Press, vol. 8(4), pages 787-827, October.
    19. Becherer, Dirk, 2003. "Rational hedging and valuation of integrated risks under constant absolute risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 33(1), pages 1-28, August.
    20. Frédéric Godin & Van Son Lai & Denis-Alexandre Trottier, 2019. "A general class of distortion operators for pricing contingent claims with applications to CAT bonds," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2019(7), pages 558-584, August.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2007.05289. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.