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An Algorithmic Approach to Discrete Time Non-homogeneous Backward Semi-Markov Reward Processes with an Application to Disability Insurance

Author

Listed:
  • Fredrik Stenberg

    (Mälardalen University)

  • Raimondo Manca

    (Università di Roma La Sapienza via del Castro Laurenziano, 9)

  • Dmitrii Silvestrov

    (Mälardalen University)

Abstract

In this paper semi-Markov reward models are presented. Higher moments of the reward process is presented for the first time applied to in time non-homogeneous semi-Markov insurance problems. Also an example is presented based on real disability data. Different algorithmic approaches to solve the problem is described.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:4:d:10.1007_s11009-006-9012-4
    DOI: 10.1007/s11009-006-9012-4
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    References listed on IDEAS

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    1. Izzet Sahin & Yves Balcer, 1979. "Stochastic Models for Pensionable Service," Operations Research, INFORMS, vol. 27(5), pages 888-903, October.
    2. Wolthuis, Henk, 1994. "Actuarial equivalence," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 163-179, December.
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    Citations

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    Cited by:

    1. Guglielmo D’Amico & Giuseppe Di Biase & Raimondo Manca, 2011. "A customer’s utility measure based on the reliability of multi-state systems," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 34(1), pages 1-20, May.
    2. 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.
    3. Guglielmo D'Amico & Montserrat Guillen & Raimondo Manca & Filippo Petroni, 2017. "Multi-state models for evaluating conversion options in life insurance," Papers 1707.01028, arXiv.org.
    4. Zacharias Kyritsis & Aleka Papadopoulou, 2017. "The Quality of Life Via Semi Markov Reward Modelling," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1029-1045, December.
    5. Guglielmo D'Amico & Raimondo Manca & Giovanni Salvi, 2012. "A Semi-Markov Modulated Interest Rate Model," Papers 1210.3164, arXiv.org.
    6. Aleka A. Papadopoulou & George Tsaklidis & Sally McClean & Lalit Garg, 2012. "On the Moments and the Distribution of the Cost of a Semi Markov Model for Healthcare Systems," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 717-737, September.
    7. Dmitrii Silvestrov & Raimondo Manca, 2017. "Reward Algorithms for Semi-Markov Processes," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1191-1209, December.
    8. F. Castella & G. Dujardin & B. Sericola, 2009. "Moments’ Analysis in Homogeneous Markov Reward Models," Methodology and Computing in Applied Probability, Springer, vol. 11(4), pages 583-601, December.
    9. Guglielmo D’Amico & Filippo Petroni & Salvatore Vergine, 2021. "An Analysis of a Storage System for a Wind Farm with Ramp-Rate Limitation," Energies, MDPI, vol. 14(13), pages 1-25, July.
    10. Guglielmo D’Amico & Filippo Petroni & Flavio Prattico, 2015. "Performance Analysis of Second Order Semi-Markov Chains: An Application to Wind Energy Production," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 781-794, September.
    11. D’Amico, Guglielmo & Manca, Raimondo & Salvi, Giovanni, 2013. "A semi-Markov modulated interest rate model," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2094-2102.
    12. 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.
    13. 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.
    14. Guglielmo D’Amico & Fulvio Gismondi & Filippo Petroni, 2020. "Insurance Contracts for Hedging Wind Power Uncertainty," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    15. 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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