Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-04-30T22:50:01.987Z Has data issue: false hasContentIssue false
  • English
  • Français

WHY DOES A HUMAN DIE? A STRUCTURAL APPROACH TO COHORT-WISE MORTALITY PREDICTION UNDER SURVIVAL ENERGY HYPOTHESIS

Published online by Cambridge University Press:  13 November 2020

Yasutaka Shimizu ,
Yuki Minami  and
Ryunosuke Ito
Yasutaka Shimizu*
Affiliation:
Department of Applied Mathematics, Waseda University, Tokyo, Japan, E-Mail: shimizu@waseda.jp
Yuki Minami
Affiliation:
Department of Applied Mathematics, Waseda University, Tokyo, Japan, E-Mails: minami-y@moegi.waseda.jp; ryunosuke.i@fuji.waseda.jp
Ryunosuke Ito
Affiliation:
Department of Applied Mathematics, Waseda University, Tokyo, Japan, E-Mails: minami-y@moegi.waseda.jp; ryunosuke.i@fuji.waseda.jp
*
E-Mail: shimizu@waseda.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We propose a new approach to mortality prediction under survival energy hypothesis (SEH). We assume that a human is born with initial energy, which changes stochastically in time and the human dies when the energy vanishes. Then, the time of death is represented by the first hitting time of the survival energy (SE) process to zero. This study assumes that SE follows a time-inhomogeneous diffusion process and defines the mortality function, which is the first hitting time distribution function of the SE process. Although SEH is a fictitious construct, we illustrate that this assumption has the potential to yield a good parametric family of cumulative probability of death, and the parametric family yields surprisingly good predictions for future mortality rates.

Keywords

Mortality predictionsurvival energy hypothesisthe first passage timediffusion processesruin theory62M8691B3060G25
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 1 , January 2021 , pp. 191 - 219
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© 2020 by Astin Bulletin. All rights reserved

References

Abbring, J.H. (2012) Mixed hitting-time models. Econometrica, 80(2), 783–819.Google Scholar
Bauer, D., Benth, F.E. and Kiesel, R. (2012) Modeling the forward surface of mortality. SIAM Journal on Financial Mathematics, 3, 639–666.CrossRefGoogle Scholar
Baukai, B. (1990) An explicit expression for the distribution of the supremum of brownian motion with a change point. Communications in Statistics - Theory and Methods, 19(1), 31–40.CrossRefGoogle Scholar
Biffis, E. (2005) Affine processes for dynamic mortality and actuarial valuation. Insurance: Mathematics and Economics, 37, 443–468.Google Scholar
Biffis, E., Denuit, M. and Devolder, P. (2010) Stochastic mortality under measure changes. Scandinavian Actuarial Journal, 2010(4), 284–311.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D. and Dowd, K. (2006) A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance, 73, 687–718.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D. and Dowd, K. (2008) Modelling and management of mortality risk: A review. Scandinavian Actuarial Journal, 2008(2–3), 79–113.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Ong, A. and Balevich, I. (2009) A quantitative comparison of stochastic mortality models using data from England & Wales and the United States. North American Actuarial Journal, 13(1), 1–35.CrossRefGoogle Scholar
Chen, H. and Cox, S.H. (2009) Modeling mortality with jumps: applications to mortality securitization. The Journal of Risk and Insurance, 76(3), 727–751.CrossRefGoogle Scholar
Dahl, M. (2004) Stochastic mortality in life insurance: Market reserves and mortality-linked insurance contracts. Insurance: Mathematics and Economics, 35, 113–136.Google Scholar
Lee, R.D. and Carter, L. (1992) Modelling and forecasting the time series of US mortality. Journal of the American Statistical Association, 87, 659–671.Google Scholar
Leng, X. and Peng, L. (2016) Inference pitfalls in Lee-Carter model for forecasting mortality. Insurance: Mathematics and Economics, 70, 58–65.Google Scholar
Hao, X., Li, X. and Shimizu, Y. (2013) Finite-time survival probability and credit default swaps pricing under geometric Lévy markets. Insurance: Mathematics and Economics, 53, 14–23.Google Scholar
Human Mortality Database: https://www.mortality.org/. Netherlands:2018.10, Sweden:2019.1, Japan:2019.8, England&Wales(civilian):2020.5.Google Scholar
Ito, R. and Shimizu, Y. (2019) Cohort-wise mortality prediction under survival energy hypothesis (in Japanese). Journakl of the Japanese Association of Risk, Insurance and Pensions (JARIP), 6, 17–30.Google Scholar
Jarrow, R.A. and Turnbull, S. (1995) Pricing derivatives on financial securities subject to credit risk. Journal of Finance, 50(1), 53–85.CrossRefGoogle Scholar
Konishi, S. and Kitagawa, G. (1996) Generalized information criteria in model selection. Biometrika, 83, 875–890.CrossRefGoogle Scholar
Lundberg, F. (1903) Approximerad Framställning av Sannolikehetsfunktionen, Aterförsäkering av Kollektivrisker. Uppsala: Almqvist & Wiksell.Google Scholar
Merton, R.C. (1974) On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance, 29(2), 449–470.Google Scholar
Merton, R. (1976) Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics, 3, 125–144.CrossRefGoogle Scholar
Molini, A., Talkner, P., Katul, G.G. and Porporato, A. (2011). First passage time statistics of Brownian motion with purely time dependent drift and diffusion. Physica A, 390, 1841–1852.CrossRefGoogle Scholar
Protter, P.E. (2004) Stochastic Integration and Differential Equations, 2nd edn. Berlin: Springer-Verlag.Google Scholar
Renshaw, A.E. and Haberman, S. (2003) Lee-Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics, 33, 255–272.Google Scholar
Renshaw, A. and Haberman, S. (2006) A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38, 556–570.Google Scholar
Schoutens, W. and Cariboni, J. (2009) Lévy Processes in Credit Risk, Podstow, UK: John Wiley & Sons.Google Scholar
van der Vaart, A.W. (1998) Asymptotic Statistics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Ye, Z. and Chen, N. (2014) The inverse Gaussian process as a degradation model. Technometrics, 56(3), 302–311.CrossRefGoogle Scholar