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Valuation and risk assessment of disability insurance using a discrete time trivariate Markov renewal reward process

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  • Maegebier, Alexander

Abstract

In disability insurance, the impact of the duration since the inception of disability on future recovery and mortality rates has been modeled by bivariate Markov renewal processes and the associated semi-Markov process, but these processes do not incorporate potential dependences between the durations in two successive states. Thus, the aim of this paper is to introduce a discrete time trivariate Markov renewal reward model, an associated formula for higher moments and a corresponding simulation that include the potential dependence between the durations, i.e. the inter-arrival times, in two successive states. The proposed model is compared with two alternative models that do not include this dependence.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:802-811
    DOI: 10.1016/j.insmatheco.2013.09.013
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    References listed on IDEAS

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    1. Hagen, Christine & Himmelreicher, Ralf K. & Kemptner, Daniel & Lampert, Thomas, 2011. "Soziale Ungleichheit und Risiken der Erwerbsminderung," WSI-Mitteilungen, Nomos Verlagsgesellschaft mbH & Co. KG, vol. 64(7), pages 336-344.
    2. 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.
    3. 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.
    4. Pitacco, Ermanno, 1995. "Actuarial models for pricing disability benefits: Towards a unifying approach," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 39-62, April.
    5. 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.
    6. Gregorius, F. K., 1993. "Disability insurance in The Netherlands," Insurance: Mathematics and Economics, Elsevier, vol. 13(2), pages 101-116, November.
    7. Amitabh Chandra & Andrew A. Samwick, 2009. "Disability Risk and the Value of Disability Insurance," NBER Chapters, in: Health at Older Ages: The Causes and Consequences of Declining Disability among the Elderly, pages 295-336, National Bureau of Economic Research, Inc.
    8. Marcus Christiansen, 2012. "Multistate models in health insurance," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(2), pages 155-186, June.
    9. 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.
    10. Segerer, Gunther, 1993. "The actuarial treatment of the disability risk in Germany, Austria and Switzerland," Insurance: Mathematics and Economics, Elsevier, vol. 13(2), pages 131-140, November.
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    Cited by:

    1. Ramírez-Cobo, Pepa & Carrizosa, Emilio & Lillo, Rosa E., 2021. "Analysis of an aggregate loss model in a Markov renewal regime," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    2. 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.
    3. Guglielmo D’Amico & Fulvio Gismondi & Filippo Petroni, 2020. "Insurance Contracts for Hedging Wind Power Uncertainty," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    4. 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.
    5. 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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    More about this item

    Keywords

    Disability insurance; Duration model; Markov reward process; Higher moments; Inter-arrival time; Dependence;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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