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Full backward non-homogeneous semi-Markov processes for disability insurance models: A Catalunya real data application

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  • D'Amico, Guglielmo
  • Guillen, Montserrat
  • Manca, Raimondo

Abstract

In this paper a stochastic model for disability insurance contracts is presented. The model is based on a discrete time non-homogeneous semi-Markov process to which the backward recurrence time process is joined. This permits us to study in a more complete way the disability evolution and to face the duration problem in a more effective way. The model is applied to a sample of contracts drawn at random from a mutual insurance company.

Suggested Citation

  • D'Amico, Guglielmo & Guillen, Montserrat & Manca, Raimondo, 2009. "Full backward non-homogeneous semi-Markov processes for disability insurance models: A Catalunya real data application," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 173-179, October.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:2:p:173-179
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    References listed on IDEAS

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    1. Janssen, J. & de Dominicis, R., 1984. "Finite non-homogeneous semi-Markov processes: Theoretical and computational aspects," Insurance: Mathematics and Economics, Elsevier, vol. 3(3), pages 157-165, July.
    2. Fredrik Stenberg & Raimondo Manca & Dmitrii Silvestrov, 2007. "An Algorithmic Approach to Discrete Time Non-homogeneous Backward Semi-Markov Reward Processes with an Application to Disability Insurance," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 497-519, December.
    3. Jacques Janssen & Raimondo Manca, 2001. "Numerical Solution of non-Homogeneous Semi-Markov Processes in Transient Case," Methodology and Computing in Applied Probability, Springer, vol. 3(3), pages 271-293, September.
    4. Izzet Sahin & Yves Balcer, 1979. "Stochastic Models for Pensionable Service," Operations Research, INFORMS, vol. 27(5), pages 888-903, October.
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    Citations

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    Cited by:

    1. Catalina Bolancé & Ramon Alemany & Montserrat Guillén, 2010. "Prediction of the economic cost of individual long-term care in the Spanish population," IREA Working Papers 201011, University of Barcelona, Research Institute of Applied Economics, revised Sep 2010.
    2. Fuino, Michel & Wagner, Joël, 2018. "Long-term care models and dependence probability tables by acuity level: New empirical evidence from Switzerland," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 51-70.
    3. D’Amico, Guglielmo & Petroni, Filippo, 2023. "ROCOF of higher order for semi-Markov processes," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    4. Hainaut, Donatien, 2021. "A fractional multi-states model for insurance," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 120-132.
    5. D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2013. "First and second order semi-Markov chains for wind speed modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1194-1201.
    6. Guglielmo D’Amico & Montserrat Guillen & Raimondo Manca, 2012. "Discrete time Non-homogeneous Semi-Markov Processes applied to Models for Disability Insurance," Working Papers XREAP2012-05, Xarxa de Referència en Economia Aplicada (XREAP), revised Mar 2012.
    7. Guglielmo D'Amico & Ada Lika & Filippo Petroni, 2019. "Risk Management of Pension Fund: A Model for Salary Evolution," IJFS, MDPI, vol. 7(3), pages 1-17, August.
    8. Maegebier, Alexander, 2013. "Valuation and risk assessment of disability insurance using a discrete time trivariate Markov renewal reward process," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 802-811.
    9. Guglielmo D’Amico & Fulvio Gismondi & Filippo Petroni, 2020. "Insurance Contracts for Hedging Wind Power Uncertainty," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    10. Andreas Niemeyer, 2015. "Safety Margins for Systematic Biometric and Financial Risk in a Semi-Markov Life Insurance Framework," Risks, MDPI, vol. 3(1), pages 1-26, January.
    11. Fuino, Michel & Wagner, Joël, 2020. "Duration of long-term care: Socio-economic factors, type of care interactions and evolution," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 151-168.
    12. Hainaut, Donatien, 2021. "A fractional multi-states model for insurance," LIDAM Discussion Papers ISBA 2021019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2017. "Insuring wind energy production," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 542-553.

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