Skip to main content

Modeling a Random Cash Flow of an Asset with a Semi-Markovian Model

  • Conference paper
  • First Online:
Data-Driven Modeling for Sustainable Engineering (ICEASSM 2017)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 72))

  • 484 Accesses

Abstract

In this paper, we use a semi-Markovian model to compute the conditional higher moments of any order of the present value of cash flows generated by an investment, taking into account the state of the market. With the force of interest following a stochastic process, we give an example to illustrate our results.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 219.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 279.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Stenberg F, Manca R, Silvestrov D (2006) Semi-Markov reward models for disability insurance. Theor Stochast Process 28:239–254

    MathSciNet  MATH  Google Scholar 

  2. Léveillé G, Adékambi F (2011) Covariance of discounted compound renewal sums with a stochastic interest rate. Scand Actuarial J 2:138–153

    Article  MathSciNet  Google Scholar 

  3. Korolyuk VS, Swishchuk A (1995) Random evolution for Semi-Markov systems. Kluwer, Dordrecht

    Book  Google Scholar 

  4. Korolyuk VS, Swishchuk A (1995b) Evolution of systems in random media. CRC Press, Boca Raton

    Google Scholar 

  5. Limnios N, Swishchuk A (2013) Discrete-time Semi-Markov random evolutions and their applications. Adv Appl Probab 45(1):214–240. https://doi.org/10.1017/s000186780000625x

    Article  MathSciNet  MATH  Google Scholar 

  6. Finkelstein M, Gertsbakh I (2015) Preventive maintenance of multistate systems subject to shocks. Appl Stochast Models Bus Ind. https://doi.org/10.1002/asmb.2151

    Article  MathSciNet  Google Scholar 

  7. Janssen J, De Dominicis R (1984) An algorithmic approach to non-homogeneous Semi-Markov Processes. Insur Math Econ 3:157–165

    Article  Google Scholar 

  8. Janssen J, Manca R (2001) Numerical solution of non-homogeneous Semi-Markov Processes in transient case. Method Comput Appl Probab 3:271–294

    Article  MathSciNet  Google Scholar 

  9. Limnios N, Oprisan G (2000) Semi-Markov Processes and reliability. Birkhauser, Boston

    Google Scholar 

  10. Pitacco E (1995) Actuarial models for pricing disability benefits: Towards a unifying approach. J Insur Math Econ 16:39–62

    Article  MathSciNet  Google Scholar 

  11. Janssen J, Limnios N (1998) Semi-Markov models and applications. In: International symposium on Semi-Markov models: theory and applications (2nd edn. Compiègne, France)

    Google Scholar 

  12. D’Amico G, Guillen M, Manca R (2012) Discrete time non-homogeneous Semi-Markov processes applied to models for disability insurance. http://www.ub.edu/ubeconomics/wp-content/uploads/2013/01/XREAP2012-05.pdf

  13. D’Amico G (2016) IMA J Manag Math 27(4). ISSN: 1471-678X Online ISSN: 1471-6798

    Google Scholar 

  14. Sansom J, Thomson PJ (2001) Fitting hidden semi-Markov models to breakpoint rainfall data. J Appl Probab 38A:142–157. https://doi.org/10.1239/jap/1085496598

    Article  MathSciNet  Google Scholar 

  15. Christiansen MC (2012) Multistate models in health insurance. Adv Stat Anal 96:155–186

    Article  MathSciNet  Google Scholar 

  16. Christiansen MC, Niemeyer A, Teigiszerova L (2015) Modeling and forecasting duration-dependent mortality rates. Comput Stat Data Anal 83:65–81

    Article  MathSciNet  Google Scholar 

  17. Jump BV, Limnios N (2008) Hidden Semi-Markov model and estimation. Semi-Markov chains and hidden Semi-Markov models toward applications. Lecture Notes in Statistics, 191

    Google Scholar 

  18. Özekici S, Soyer R (2006) Math Meth Oper Res 64:125. https://doi.org/10.1007/s00186-006-0067-3

    Article  Google Scholar 

  19. Yu S-Z (2015) Hidden Semi-Markov models: theory, algorithms and applications, 1st edn. Publisher: Elsevier, 208 pages. ISBN 978-0128027677

    Chapter  Google Scholar 

  20. Yu S-Z (2010) Hidden Semi-Markov models. Artif Intell 174(2):215–243. https://doi.org/10.1016/j.artint.2009.11.011

    Article  MathSciNet  Google Scholar 

  21. Segerer G (1993) The actuarial treatment of the disability risk in Germany, Austria and Switzerland. Insur Math Econ 13:131–140

    MATH  Google Scholar 

  22. Gram JP (1910) Professor Thiele som aktuar. Dansk Forsikringsårbog, pp 26–37

    Google Scholar 

  23. Jørgensen NR (1913) Grundzüge einer Theorie der Lebensversicherung. G. Fischer

    Google Scholar 

  24. Hoem JM (1972) Inhomogeneous semi-Markov processes, select actuarial tables, and duration-dependence in demography. Population dynamics. Academic Press, New York, pp 251–296

    Chapter  Google Scholar 

  25. Helwich M (2008) Durational effects and non-smooth semi-Markov models in life insurance. Doctoral dissertation, University of Rostock. urn:nbn:de:gbv:28-diss2008-0056-4. http://rosdok.uni-rostock.de/

  26. Hoem JM (1969) Markov chain models in life insurance. Blätterder DGVFM 9:91–107

    Article  Google Scholar 

  27. Amsler MH (1968) Les chaines de Markov des assurances vie, invalidité et maladie. In: Transactions of the 18th international congress of actuaries, München, vol 5, pp 731–746

    Google Scholar 

  28. Norberg R (1991) Reserves in life pension insurance. Scand Actuarial J, pp 3–24

    Google Scholar 

  29. Norberg R (1992) Hattendorf’s theorem and Thiele’s differential equation generalized. Scand Actuarial J, pp 2–14

    Article  MathSciNet  Google Scholar 

  30. Norberg R (1995) Differential equations for moments of present values in life insurance. Insur Math Econ 17:171–180

    Article  MathSciNet  Google Scholar 

  31. Adékambi F, Christiensen M (2017) Integral and differential equations for the moments of multistate models in health insurance. Scand Actuarial J 1:29–50

    Article  MathSciNet  Google Scholar 

  32. Pyke R (1961) Markov renewal processes with finitely many states. Ann Math Stat 32(4):1243–1259

    Article  MathSciNet  Google Scholar 

  33. Norberg R, Moller CM (1996) Thiele’s differential equations with stochastic interest of diffusion type. Scan Actuarial J 1:37–49

    Article  MathSciNet  Google Scholar 

  34. Chung KL, Williams RJ (1990) 2nd edn. Birkhauser, Boston

    Google Scholar 

  35. Andersen PK, Borgan Ø, Gill RD, Keiding N (1993) Statistical models based on counting processes. Springer, Berlin, Heidelberg

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Franck Adékambi .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Adékambi, F. (2020). Modeling a Random Cash Flow of an Asset with a Semi-Markovian Model. In: Adjallah, K., Birregah, B., Abanda, H. (eds) Data-Driven Modeling for Sustainable Engineering. ICEASSM 2017. Lecture Notes in Networks and Systems, vol 72. Springer, Cham. https://doi.org/10.1007/978-3-030-13697-0_8

Download citation

Publish with us

Policies and ethics