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Stenberg, Fredrik; Manca, Raimondo; Silvestrov, Dmitrii

An algorithmic approach to discrete time non-homogeneous backward semi-Markov reward processes with an application to disability insurance. (English) Zbl 1146.60320

Methodol. Comput. Appl. Probab. 9, No. 4, 497-519 (2007).
Summary: 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.

Cited in 17 Documents

MSC:

60K15 Markov renewal processes, semi-Markov processes
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
91B30 Risk theory, insurance (MSC2010)

Keywords:

semi-Markov process; discrete time; actuarial; higher moments; variance; reward process; skewness; kurtosis
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References:

[1] Y. Balcer, and I. Sahin, ”Pension accumulation as a semi-Markov reward process, with applications to pension reform.” In J. Janssen (eds), Semi-Markov Models, Plenum: New York, 1986.
[2] A. Blasi, J. Janssen, and R. Manca, ”Generalized discrete time homogeneous stochastic annuities and multi-state insurance model,” In Proceedings of IME 2004, Rome, Italy, 2004. · Zbl 1114.60327
[3] CMIR12, (Continuous Mortality Investigation Report, no. 12), ”The analysis of permanent health insurance data,” The Institute of Actuaries and the Faculty of Actuaries, 1991.
[4] R. Consael, and J. Sonnenscheim, ”Theorie mathematique des assurances des personnes. Modèle markovien,” Mitteilungen der Vereinigung schweizerischer Versincherungsmathematik vol.78 pp. 75–93, 1978. · Zbl 0386.62089
[5] E. Çinlar, ”Markov renewal theory,” Advances in Applied Probability vol. 1 pp. 123–187, 1969. · Zbl 0212.49601 · doi:10.2307/1426216
[6] R. De Dominicis, and R. Manca, ”An algorithmic approach to non-homogeneous semi-Markov processes,” Communications in Statistics. Simulation and Computation vol.13 pp. 113–127, 1984. · Zbl 0568.60084
[7] R. De Dominicis, and R. Manca, ”Some new results on the transient behaviour of semi-Markov reward processes,” Methods of Operations Research vol. 54, 1986. · Zbl 0594.60091
[8] R. De Dominicis, R. Manca, and L. Granata, ”The dynamics of pension funds in a stochastic environment,” Scandinavian Actuarial Journal 1991. · Zbl 0778.62095
[9] S. Haberman, and E. Pitacco, Actuarial Models for Disability Insurance, Chapman and Hall: London, UK, 1999. · Zbl 0935.62118
[10] J. M. Hoem, ”Markov chain models in life insurance,” Blätter der Deutschen Gesellschaft für Versincherungsmathematik vol. 9 pp. 91–107, 1969. · Zbl 0191.51103
[11] J. M. Hoem, ”Inhomogeneous semi-Markov processes, select actuarial tables, and duration-dependence in demography.” In T.N.E. Greville (ed.), Population, Dynamics, pp. 251–296, Academic: NY, 1972.
[12] J. M. Hoem, ”The versatility of the Markov chain as a tool in the mathematics of life insurance,” Transactions of the 23rd Congress of Actuaries vol. R pp. 141–202, 1988.
[13] A. Iosifescu Manu, ”Non homogeneous semi-Markov processes,” Stud. Lere. Mat. vol. 24 pp. 529–533, 1972. · Zbl 0245.60067
[14] J. Janssen, ”Application des processus semi-markoviens à un probléme d’invalidité,” Bulletin de l’Association Royale des Actuaries Belges vol. 63 pp. 35–52, 1966.
[15] J. Janssen, and R. De Dominicis, ”Finite non-homogeneous semi-Markov processes,” Insurance: Mathematics and Economics vol. 3 pp. 157–165, 1984. · Zbl 0546.60087 · doi:10.1016/0167-6687(84)90057-X
[16] J. Janssen, and R. Manca, ”A realistic non-homogeneous stochastic pension funds model on scenario basis,” Scandinavian Actuarial Journal vol. 2 pp. 113–137, 1997. · Zbl 1078.62531
[17] J. Janssen, and R. Manca, ”General actuarial models in a semi-Markov environment,” In Proceedings of ICA Cancun 2002, Mexico, 2002. · Zbl 1050.91044
[18] J. Janssen, and R. Manca, ”Multi-state insurance model description by means of continuous time homogeneous semi-Markov reward processes,” Mimeo, 2003.
[19] J. Janssen, and R. Manca, ”Discrete time non-homogeneous semi-Markov reward processes, generalized stochastic annuities and multi-state insurance model,” In Proceedings of XXVIII AMASES, Modena, 2004.
[20] J. Janssen, and R. Manca, Applied Semi-Markov Processes, Springer, Berlin Heidelberg New York, 2006. · Zbl 1096.60002
[21] J. Janssen, R. Manca, and E. Volpe di Prignano, ”Continuous time non homogeneous semi-Markov reward processes and multi-state insurance application,” In Proceedings of IME 2004, 2004. · Zbl 1301.60103
[22] R. Manca, D. Silvestrov, F. Stenberg, ”Homogeneous Backward Semi-Markov Reward Models for Insurance Contracts,” In Procedings Applied Stochastic Models and Data Analysis 2005, ISBN 2-908849-15-1, 2005. · Zbl 1141.60056
[23] C. M. Moller, ”Numerical evaluation of Markov transition probabilities based on the discretized product integral,” Scandinavian Actuarial Journal pp. 76–87, 1992. · Zbl 0761.65109
[24] R. Norberg, ”Identities for present values of life insurance benefits,” Scandinavian Actuarial Journal pp. 100–106, 1993. · Zbl 0792.62095
[25] I. Sahin, and Y. Balcer, ”Stochastic models for a pensionable service,” Operational Research vol. 27 pp. 888–903, 1979.
[26] F. Stenberg, R. Manca, and D. Silvestrov, ”Discrete time backward semi-Markov reward processes and an application to disability insurance problems,” Research Report 2005-1 Department of Mathematics and Physics, Mälardalen University, Sweden, 1–44, ISSN 1494-4978, 2005. · Zbl 1146.60320
[27] F. Stenberg, R. Manca, and D. Silvestrov, ”Discrete time homogenous backward semi-Markov reward processes and an application to disability insurance,” 2005. · Zbl 1146.60320
[28] H. Waters, ”An approach for the study of multiple state models,” Journal of the Institute of Actuaries vol. 116 pp. 611–624, 1984.
[29] H. Wolthuis, ”Actuarial equivalence,” Insurance: Mathematics and Economics vol. 15 pp. 163–179, 1994. · Zbl 0820.62091 · doi:10.1016/0167-6687(94)90792-7
[30] H. Wolthuis, Life Insurance Mathematics (The Markovian Model) IAE, Universiteit van Amsterdam, Amsterdam II edition, 2003.
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