IDEAS home Printed from https://ideas.repec.org/a/spr/lifeda/v29y2023i1d10.1007_s10985-022-09577-1.html
   My bibliography  Save this article

A uniformisation-driven algorithm for inference-related estimation of a phase-type ageing model

Author

Listed:
  • Boquan Cheng

    (The University of Western Ontario)

  • Rogemar Mamon

    (The University of Western Ontario
    University of the Philippines Visayas)

Abstract

We develop an efficient algorithm to compute the likelihood of the phase-type ageing model. The proposed algorithm uses the uniformisation method to stabilise the numerical calculation. It also utilises a vectorised formula to only calculate the necessary elements of the probability distribution. Our algorithm, with an error’s upper bound, could be adjusted easily to tackle the likelihood calculation of the Coxian models. Furthermore, we compare the speed and the accuracy of the proposed algorithm with those of the traditional method using the matrix exponential. Our algorithm is faster and more accurate than the traditional method in calculating the likelihood. Based on our experiments, we recommend using 20 sets of randomly-generated initial values for the optimisation to get a reliable estimate for which the evaluated likelihood is close to the maximum likelihood.

Suggested Citation

  • Boquan Cheng & Rogemar Mamon, 2023. "A uniformisation-driven algorithm for inference-related estimation of a phase-type ageing model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(1), pages 142-187, January.
    • Handle: RePEc:spr:lifeda:v:29:y:2023:i:1:d:10.1007_s10985-022-09577-1
    DOI: 10.1007/s10985-022-09577-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10985-022-09577-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10985-022-09577-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Adele H. Marshall & Mariangela Zenga, 2012. "Experimenting with the Coxian Phase-Type Distribution to Uncover Suitable Fits," Methodology and Computing in Applied Probability, Springer, vol. 14(1), pages 71-86, March.
    2. Søren Asmussen & Patrick J. Laub & Hailiang Yang, 2019. "Phase-Type Models in Life Insurance: Fitting and Valuation of Equity-Linked Benefits," Risks, MDPI, vol. 7(1), pages 1-22, February.
    3. X. Lin & Xiaoming Liu, 2007. "Markov Aging Process and Phase-Type Law of Mortality," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 92-109.
    4. Donald Gross & Douglas R. Miller, 1984. "The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes," Operations Research, INFORMS, vol. 32(2), pages 343-361, April.
    5. M. Govorun & B. L. Jones & X. Liu & D. A. Stanford, 2018. "Physiological Age, Health Costs, and Their Interrelation," North American Actuarial Journal, Taylor & Francis Journals, vol. 22(3), pages 323-340, July.
    6. Su, Shu & Sherris, Michael, 2012. "Heterogeneity of Australian population mortality and implications for a viable life annuity market," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 322-332.
    7. Siu, Chi Chung & Yam, Sheung Chi Phillip & Yang, Hailiang, 2015. "Valuing Equity-Linked Death Benefits In A Regime-Switching Framework," ASTIN Bulletin, Cambridge University Press, vol. 45(2), pages 355-395, May.
    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. Milevsky, Moshe A., 2020. "Calibrating Gompertz in reverse: What is your longevity-risk-adjusted global age?," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 147-161.
    2. Albrecher Hansjörg & Bladt Martin & Müller Alaric J. A., 2023. "Joint lifetime modeling with matrix distributions," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-22, January.
    3. Annamaria Olivieri & Ermanno Pitacco, 2016. "Frailty and Risk Classification for Life Annuity Portfolios," Risks, MDPI, vol. 4(4), pages 1-23, October.
    4. Franck Adékambi, 2019. "Moments Of Phase-Type Aging Modeling For Health Dependent Costs," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(2), pages 37-64, June.
    5. Wenguang Yu & Yaodi Yong & Guofeng Guan & Yujuan Huang & Wen Su & Chaoran Cui, 2019. "Valuing Guaranteed Minimum Death Benefits by Cosine Series Expansion," Mathematics, MDPI, vol. 7(9), pages 1-15, September.
    6. Søren Asmussen & Patrick J. Laub & Hailiang Yang, 2019. "Phase-Type Models in Life Insurance: Fitting and Valuation of Equity-Linked Benefits," Risks, MDPI, vol. 7(1), pages 1-22, February.
    7. Meyricke, Ramona & Sherris, Michael, 2013. "The determinants of mortality heterogeneity and implications for pricing annuities," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 379-387.
    8. Khouzeima Moutanabbir & Hassan Abdelrahman, 2022. "Bivariate Sarmanov Phase-Type Distributions for Joint Lifetimes Modeling," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1093-1118, June.
    9. Albrecher, Hansjörg & Bladt, Martin & Bladt, Mogens & Yslas, Jorge, 2022. "Mortality modeling and regression with matrix distributions," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 68-87.
    10. Deelstra, Griselda & Hieber, Peter, 2023. "Randomization and the valuation of guaranteed minimum death benefits," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1218-1236.
    11. Yaodi Yong & Hailiang Yang, 2021. "Valuation of Cliquet-Style Guarantees with Death Benefits in Jump Diffusion Models," Mathematics, MDPI, vol. 9(16), pages 1-21, August.
    12. Riccardo De Bin & Vegard Grødem Stikbakke, 2023. "A boosting first-hitting-time model for survival analysis in high-dimensional settings," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(2), pages 420-440, April.
    13. Víctor Suñé, 2017. "Computing the Expected Markov Reward Rates with Stationarity Detection and Relative Error Control," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 445-485, June.
    14. Godin, Frédéric & Lai, Van Son & Trottier, Denis-Alexandre, 2019. "Option pricing under regime-switching models: Novel approaches removing path-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 130-142.
    15. Kirkby, J. Lars & Nguyen, Duy, 2021. "Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 408-428.
    16. Christian Acal & Juan E. Ruiz-Castro & David Maldonado & Juan B. Roldán, 2021. "One Cut-Point Phase-Type Distributions in Reliability. An Application to Resistive Random Access Memories," Mathematics, MDPI, vol. 9(21), pages 1-13, October.
    17. M. Arns & P. Buchholz & A. Panchenko, 2010. "On the Numerical Analysis of Inhomogeneous Continuous-Time Markov Chains," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 416-432, August.
    18. Bruszas, Sandy & Kaschützke, Barbara & Maurer, Raimond & Siegelin, Ivonne, 2018. "Unisex pricing of German participating life annuities—Boon or bane for customer and insurance company?," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 230-245.
    19. Hainaut, Donatien, 2016. "Impact of volatility clustering on equity indexed annuities," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 367-381.
    20. Govorun, Maria & Latouche, Guy & Loisel, Stéphane, 2015. "Phase-type aging modeling for health dependent costs," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 173-183.

    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:spr:lifeda:v:29:y:2023:i:1:d:10.1007_s10985-022-09577-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.