Multi-state models for evaluating conversion options in life insurance

Guglielmo D'Amico, Montserrat Guillen, Raimondo Manca, Filippo Petroni

Abstract


In this paper we propose a multi-state model for the evaluation of the conversion option contract. The multi-state model is based on age-indexed semi-Markov chains that are able to reproduce many important aspects that influence the valuation of the option such as the duration problem, the time non-homogeneity and the ageing effect. The value of the conversion option is evaluated after the formal description of this contract.

Keywords


Semi-Markov chain; temporary insurance policy; permanent insurance policy

Full Text:

PDF

References


[1] D’Amico, G.: Age-usage semi-Markov models. Appl. Math. Model. 35, 4354–4366 (2011). MR2801959. doi:10.1016/j.apm.2011.03.006

[2] D’Amico, G., Petroni, F.: A semi-Markov model with memory for price changes. J. Stat. Mech. Theory Exp., P12009 (2011)

[3] D’Amico, G., Petroni, F.: Weighted-indexed semi-Markov models for modeling financial returns. J. Stat. Mech. Theory Exp., P07015 (2011)

[4] D’Amico, G., Guillen, M., Manca, R.: Full backward non-homogeneous semi-Markov processes for disability insurance models: A Catalunya real data application. Insur. Math. Econ. 45, 173–179 (2009). MR2583371. doi:10.1016/j.insmatheco.2009.05.010

[5] D’Amico, G., Guillen, M., Manca, R.: Semi-Markov disability insurance models. Commun. Stat., Theory Methods 42(16), 2172–2188 (2013). MR3170905. doi:10.1080/03610926.2012.746982

[6] D’Amico, G., Janssen, J., Manca, R.: Discrete time non-homogeneous semi-Markov reliability transition credit risk models and the default distribution functions. Comput. Econ. 38, 465–481 (2011)

[7] D’Amico, G., Di Biase, G., Janssen, J., Manca, R.: HIV evolution: A quantification of the effects due to age and to medical progress. Informatica 22(1), 27–42 (2011). MR2885657

[8] Haberman, S., Pitacco, E.: Actuarial Models for Disability Insurance. Chapman & Hall, London (1999). MR1653961

[9] Janssen, J., Manca, R.: A realistic non-homogeneous stochastic pension funds model on scenario basis. Scand. Actuar. J. 2, 113–137 (1997)

[10] Kwon, H.S., Jones, B.: The impact of the determinants of mortality on life insurance and annuities. Insur. Math. Econ. 38, 271–288 (2006). MR2212527. doi:10.1016/j.insmatheco.2005.08.007

[11] Kwon, H.S., Jones, B.: Applications of a multi-state risk factor/mortality model in life insurance. Insur. Math. Econ. 43, 394–402 (2008). MR2479585. doi:10.1016/j.insmatheco.2008.07.004

[12] Lin, X.S., Liu, X.: Markov aging process and phase-type law of mortality. N. Am. Actuar. J. 11, 92–109 (2007). MR2413621. doi:10.1080/10920277.2007.10597486

[13] Liu, X., Lin, X.S.: A subordinated Markov model for stochastic mortality. Eur. Actuar. J. 2, 105–127 (2012). MR2954471. doi:10.1007/s13385-012-0047-3

[14] Maegebier, A.: Valuation and risk assessment of disability insurance using a discrete time trivariate Markov renewal reward process. Insur. Math. Econ. 53, 802–811 (2013). MR3130475. doi:10.1016/j.insmatheco.2013.09.013

[15] Nordahl, H.A.: Valuation of life insurance surrender and exchange options. Insur. Math. Econ. 42, 909–919 (2008). MR2435361. doi:10.1016/j.insmatheco.2007.10.011

[16] Stenberg, F., Manca, R., Silvestrov, D.: An algorithmic approach to discrete time non-homogeneous backward semi-Markov reward processes with an application to disability insurance. Methodol. Comput. Appl. Probab. 9, 497–519 (2007). MR2404740. doi:10.1007/s11009-006-9012-4

[17] Su, K.C.: The conversion option in life insurance. Insur. Math. Econ. 46, 437–442 (2010). MR2642520. doi:10.1016/j.insmatheco.2009.12.009

[18] Tolley, H.D., Manton, K.G.: Intervention effects among a collection of risks. Trans. Soc. Actuar. 43, 443–467 (1991)




DOI: http://dx.doi.org/10.15559/17-VMSTA78

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Guglielmo D'Amico, Montserrat Guillen, Raimondo Manca, Filippo Petroni

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.