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On a Retarded Nonlocal Ordinary Differential System with Discrete Diffusion Modeling Life Tables

Author

Listed:
  • Francisco Morillas

    (Departament d’Economia Aplicada, Facultat d’Economia, Campus dels Tarongers s/n, Universitat de València, 46022 València, Spain)

  • José Valero

    (Centro de Investigación Operativa, Avda. Universidad s/n, Universidad Miguel Hernández de Elche, 03202 Elche, Spain)

Abstract

In this paper, we consider a system of ordinary differential equations with non-local discrete diffusion and finite delay and with either a finite or an infinite number of equations. We prove several properties of solutions such as comparison, stability and symmetry. We create a numerical simulation showing that this model can be appropriate to model dynamical life tables in actuarial or demographic sciences. In this way, some indicators of goodness and smoothness are improved when comparing with classical techniques.

Suggested Citation

  • Francisco Morillas & José Valero, 2021. "On a Retarded Nonlocal Ordinary Differential System with Discrete Diffusion Modeling Life Tables," Mathematics, MDPI, vol. 9(3), pages 1-27, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:220-:d:485238
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    References listed on IDEAS

    as
    1. Haberman, Steven & Renshaw, Arthur, 2009. "On age-period-cohort parametric mortality rate projections," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 255-270, October.
    2. Debón, A. & Montes, F. & Puig, F., 2008. "Modelling and forecasting mortality in Spain," European Journal of Operational Research, Elsevier, vol. 189(3), pages 624-637, September.
    3. Haberman, Steven & Renshaw, Arthur, 2013. "Modelling and projecting mortality improvement rates using a cohort perspective," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 150-168.
    4. Xiao Dong & Brandon Milholland & Jan Vijg, 2016. "Evidence for a limit to human lifespan," Nature, Nature, vol. 538(7624), pages 257-259, October.
    5. Gavin, John & Haberman, Steven & Verrall, Richard, 1993. "Moving weighted average graduation using kernel estimation," Insurance: Mathematics and Economics, Elsevier, vol. 12(2), pages 113-126, April.
    6. Haberman, Steven & Renshaw, Arthur, 2012. "Parametric mortality improvement rate modelling and projecting," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 309-333.
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