Modern Stochastics: Theory and Applications logo


  • Help
Login Register

  1. Home
  2. Issues
  3. Volume 4, Issue 2 (2017)
  4. Multi-state models for evaluating conver ...

Modern Stochastics: Theory and Applications

Submit your article Information Become a Peer-reviewer
  • Article info
  • Full article
  • Cited by
  • More
    Article info Full article Cited by

Multi-state models for evaluating conversion options in life insurance✩
Volume 4, Issue 2 (2017), pp. 127–139
Guglielmo D’Amico ORCID icon link to view author Guglielmo D’Amico details   Montserrat Guillen   Raimondo Manca   Filippo Petroni  

Authors

 
Placeholder
https://doi.org/10.15559/17-VMSTA78
Pub. online: 10 May 2017      Type: Research Article      Open accessOpen Access

✩ This work is dedicated to Prof. Dmitrii Silvestrov in recognition of his contribution to actuarial mathematics.

Received
29 March 2017
Revised
20 April 2017
Accepted
21 April 2017
Published
10 May 2017

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.

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)

Full article Cited by PDF XML
Full article Cited by PDF XML

Copyright
© 2017 The Author(s). Published by VTeX
by logo by logo
Open access article under the CC BY license.

Keywords
Semi-Markov chain temporary insurance policy permanent insurance policy

MSC2010
60K15 90B25

Metrics
since March 2018
626

Article info
views

306

Full article
views

361

PDF
downloads

187

XML
downloads

Export citation

Copy and paste formatted citation
Placeholder

Download citation in file


Share


RSS

MSTA

MSTA

  • Online ISSN: 2351-6054
  • Print ISSN: 2351-6046
  • Copyright © 2018 VTeX

About

  • About journal
  • Indexed in
  • Editors-in-Chief

For contributors

  • Submit
  • OA Policy
  • Become a Peer-reviewer

Contact us

  • ejournals-vmsta@vtex.lt
  • Mokslininkų 2A
  • LT-08412 Vilnius
  • Lithuania
Powered by PubliMill  •  Privacy policy