IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/112754.html
   My bibliography  Save this paper

A Cox model for gradually disappearing events

Author

Listed:
  • Jang, Jiwook
  • Qu, Yan
  • Zhao, Hongbiao
  • Dassios, Angelos

Abstract

Innovations in medicine provide us longer and healthier life, leading lower mortality. Sooner rather than later, much greater longevity would be possible for us due to artificial intelligence advances in health care. Similarly, Advanced Driver Assistance Systems (ADAS) in highly automated vehicles may reduce or even eventually eliminate accidents by perceiving dangerous situations, which would minimize the number of accidents and lead to fewer loss claims for insurance companies. To model the survivor function capturing greater longevity as well as the number of claims reflecting less accidents in the long run, in this paper, we study a Cox process whose intensity process is piecewise-constant and decreasing. We derive its ultimate distributional properties, such as the Laplace transform of intensity integral process, the probability generating function of point process, their associated moments and cumulants, and the probability of no more claims for a given time point. In general, this simple model may be applicable in many other areas for modeling the evolution of gradually disappearing events, such as corporate defaults, dividend payments, trade arrivals, employment of a certain job type (e.g., typists) in the labor market, and release of particles. In particular, we discuss some potential applications to insurance.

Suggested Citation

  • Jang, Jiwook & Qu, Yan & Zhao, Hongbiao & Dassios, Angelos, 2023. "A Cox model for gradually disappearing events," LSE Research Online Documents on Economics 112754, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:112754
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/112754/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Daniel Dufresne, 2000. "Laguerre Series for Asian and Other Options," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 407-428, October.
    2. Basu, Sankarshan & Dassios, Angelos, 2002. "A Cox process with log-normal intensity," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 297-302, October.
    3. Badescu, Andrei L. & Lin, X. Sheldon & Tang, Dameng, 2016. "A marked Cox model for the number of IBNR claims: Theory," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 29-37.
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    6. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    7. Jiwook Jang & Siti Norafidah Mohd Ramli, 2018. "Hierarchical Markov Model in Life Insurance and Social Benefit Schemes," Risks, MDPI, vol. 6(3), pages 1-17, June.
    8. Angelos Dassios & Jayalaxshmi Nagaradjasarma, 2006. "The square-root process and Asian options," Quantitative Finance, Taylor & Francis Journals, vol. 6(4), pages 337-347.
    9. 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.
    10. Dassios, Angelos & Jang, Jiwook, 2003. "Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity," LSE Research Online Documents on Economics 2849, London School of Economics and Political Science, LSE Library.
    11. Park, Jong Jun & Jang, Hyun Jin & Jang, Jiwook, 2020. "Pricing arithmetic Asian options under jump diffusion CIR processes," Finance Research Letters, Elsevier, vol. 34(C).
    12. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2015. "A risk model with renewal shot-noise Cox process," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 55-65.
    13. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    14. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    15. LUCIANO, Elisa & VIGNA, Elena, 2008. "Mortality risk via affine stochastic intensities: calibration and empirical relevance," MPRA Paper 59627, University Library of Munich, Germany.
    16. Jang, Jiwook & Dassios, Angelos & Zhao, Hongbiao, 2018. "Moments of renewal shot-noise processes and their applications," LSE Research Online Documents on Economics 87428, London School of Economics and Political Science, LSE Library.
    17. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2015. "A risk model with renewal shot-noise Cox process," LSE Research Online Documents on Economics 64051, London School of Economics and Political Science, LSE Library.
    18. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
    19. Ning Cai & Steven Kou, 2012. "Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model," Operations Research, INFORMS, vol. 60(1), pages 64-77, February.
    20. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
    21. Hansjörg Albrecher & José Carlos Araujo-Acuna & Jan Beirlant, 2021. "Fitting Nonstationary Cox Processes: An Application to Fire Insurance Data," North American Actuarial Journal, Taylor & Francis Journals, vol. 25(2), pages 135-162, April.
    22. Dassios, Angelos & Nagaradjasarma, Jayalaxshmi, 2006. "The square-root process and Asian options," LSE Research Online Documents on Economics 2851, London School of Economics and Political Science, LSE Library.
    23. Basu, Sankarshan & Dassios, Angelos, 2002. "A Cox process with log-normal intensity," LSE Research Online Documents on Economics 16375, London School of Economics and Political Science, LSE Library.
    24. Jarrow, Robert A., 2010. "A simple robust model for Cat bond valuation," Finance Research Letters, Elsevier, vol. 7(2), pages 72-79, June.
    25. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    26. Jang, Jiwook & Mohd Ramli, Siti Norafidah, 2015. "Jump diffusion transition intensities in life insurance and disability annuity," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 440-451.
    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. Yang Chang & Michael Sherris, 2018. "Longevity Risk Management and the Development of a Value-Based Longevity Index," Risks, MDPI, vol. 6(1), pages 1-20, February.
    2. Luciano, Elisa & Regis, Luca & Vigna, Elena, 2012. "Delta–Gamma hedging of mortality and interest rate risk," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 402-412.
    3. Russo, Vincenzo & Giacometti, Rosella & Ortobelli, Sergio & Rachev, Svetlozar & Fabozzi, Frank J., 2011. "Calibrating affine stochastic mortality models using term assurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 53-60, July.
    4. Leunglung Chan & Eckhard Platen, 2016. "Pricing of long dated equity-linked life insurance contracts," Published Paper Series 2016-5, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    5. Elisa Luciano & Luca Regis & Elena Vigna, 2011. "Delta and Gamma hedging of mortality and interest rate risk," ICER Working Papers - Applied Mathematics Series 01-2011, ICER - International Centre for Economic Research.
    6. Marcus C. Christiansen, 2013. "Gaussian and Affine Approximation of Stochastic Diffusion Models for Interest and Mortality Rates," Risks, MDPI, vol. 1(3), pages 1-20, October.
    7. Jiwook Jang & Jong Jun Park & Hyun Jin Jang, 2018. "Catastrophe Insurance Derivatives Pricing Using A Cox Process With Jump Diffusion Cir Intensity," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-20, November.
    8. Dassios, Angelos & Zhao, Hongbiao, 2017. "Efficient simulation of clustering jumps with CIR intensity," LSE Research Online Documents on Economics 74205, London School of Economics and Political Science, LSE Library.
    9. Angelos Dassios & Hongbiao Zhao, 2017. "Efficient Simulation of Clustering Jumps with CIR Intensity," Operations Research, INFORMS, vol. 65(6), pages 1494-1515, December.
    10. Braun, Alexander, 2011. "Pricing catastrophe swaps: A contingent claims approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 520-536.
    11. Alan Genaro & Adilson Simonis, 2015. "Estimating doubly stochastic Poisson process with affine intensities by Kalman filter," Statistical Papers, Springer, vol. 56(3), pages 723-748, August.
    12. Anastasia Novokreshchenova, 2016. "Predicting Human Mortality: Quantitative Evaluation of Four Stochastic Models," Risks, MDPI, vol. 4(4), pages 1-28, December.
    13. Georgina Onuma Kalu & Chinemerem Dennis Ikpe & Benjamin Ifeanyichukwu Oruh & Samuel Asante Gyamerah, 2020. "State Space Vasicek Model of a Longevity Bond," Papers 2011.12753, arXiv.org.
    14. 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.
    15. Stefan Tappe & Stefan Weber, 2019. "Stochastic mortality models: An infinite dimensional approach," Papers 1907.05157, arXiv.org.
    16. Jevtić, Petar & Luciano, Elisa & Vigna, Elena, 2013. "Mortality surface by means of continuous time cohort models," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 122-133.
    17. Liang, Zongxia & Sheng, Wenlong, 2016. "Valuing inflation-linked death benefits under a stochastic volatility framework," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 45-58.
    18. Melnikov, Alexander & Romaniuk, Yulia, 2006. "Evaluating the performance of Gompertz, Makeham and Lee-Carter mortality models for risk management with unit-linked contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 310-329, December.
    19. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin, 2006. "Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 79-120, May.
    20. Yiqing Chen, 2019. "A Renewal Shot Noise Process with Subexponential Shot Marks," Risks, MDPI, vol. 7(2), pages 1-8, June.

    More about this item

    Keywords

    Point process; Cox process; Cox process with piecewise-constant decreasing intensity; gradually disappearing events; survival probability; competing risks; stop-loss reinsurance;
    All these keywords.

    JEL classification:

    • R14 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Land Use Patterns
    • J01 - Labor and Demographic Economics - - General - - - Labor Economics: General

    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:ehl:lserod:112754. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    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.