Soft Computing

, Volume 22, Issue 12, pp 4123–4131 | Cite as

The mean chance of ultimate ruin time in random fuzzy insurance risk model

  • Sara GhasemalipourEmail author
  • Behrouz Fathi-Vajargah
Methodologies and Application


In this paper, we study a modified risk model in which both the claim amount and premium are assumed to be random fuzzy variables. In this risk model, some new theorems concerning the mean chance of ultimate ruin time are proved in two cases where the initial surplus is zero and nonzero. Finally, a numerical example is mentioned to illustrate the method.


Risk model Renewal process Random fuzzy variable Mean chance of ruin 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Ammeter H (1948) A generalization of the collective theory of risk in regard to fluctuating basic probabilities. Skand Aktuarietidskr 34:171–198MathSciNetzbMATHGoogle Scholar
  2. Andersen E (1957) On the collective theory of risk in case of contagion betten claims. Bull Inst Math Appl 12:275–279Google Scholar
  3. Boutsikas MV, Rakitzis AC, Antzoulakos DL (2016) On the number of claims until ruin in a two-barrier renewal risk model with Erlang mixtures. J Comput Appl Math 294:124–137MathSciNetCrossRefzbMATHGoogle Scholar
  4. Dickson D (1998) On a class of renewal risk process. N Am Actuar J 2:60–68MathSciNetCrossRefzbMATHGoogle Scholar
  5. Dickson D, Hipp C (1998) Ruin probabilities for Erlang (2) risk process. Insur Math Econ 22:251–262CrossRefzbMATHGoogle Scholar
  6. Dong H, Liu Z (2013) The ruin problem in a renewal risk model with two-sided jumps. Math Comput Model 57:800–811MathSciNetCrossRefzbMATHGoogle Scholar
  7. Gerber H (1979) An introduction to mathematical risk theory. Philadelphia: S. S. Heubner Foundation monograph series 8Google Scholar
  8. Huang T, Zhao R, Tang W (2009) Risk model with fuzzy random individual claim amount. Eur J Oper Res 192:879–890MathSciNetCrossRefzbMATHGoogle Scholar
  9. Huang T, Diao J (2010) Risk model in fuzzy random environments. In: Intelligent computing and intelligent systems (ICIS), 2010 IEEE international conferenceGoogle Scholar
  10. Huang T, Diao J, Wei Zh (2011) Inequality for mean chance of ultimate ruin in risk model with random fuzzy theory. In: Emergency management and management sciences (ICEMMS), 2nd IEEE international conferenceGoogle Scholar
  11. Huang T, Wei Z, Diao J (2011) Risk model with random fuzzy theory. In: The 13th IEEE joint international computer science and information technology conferenceGoogle Scholar
  12. Li J, Dickson D, Li S (2015) Some ruin problems for the MAP risk model. Insur Math Econ 65:1–8MathSciNetCrossRefzbMATHGoogle Scholar
  13. Li S, Garrido J (2004) On ruin for the Erlang(n) risk process. Insur Math Econ 34:391–408MathSciNetCrossRefzbMATHGoogle Scholar
  14. Liu B (2002) Theory and practice of uncertain programming. Physica, HeidelbergCrossRefzbMATHGoogle Scholar
  15. Liu B (2004) Uncertainty theory. Springer, BerlinCrossRefGoogle Scholar
  16. Liu B (2007) Uncertainty theory, 2nd edn. Springer, BerlinzbMATHGoogle Scholar
  17. Liu B, Liu Y (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans Fuzzy Syst 10:445–450CrossRefGoogle Scholar
  18. Liu YK, Liu BD (2003) Expected value operator of random fuzzy variable and random fuzzy expected value models. Int J Uncertain Fuzziness Knowl Based Syst 11:195–215Google Scholar
  19. Liu Y, Liu B (2003) Fuzzy random variables: a scalar expected value operator. Fuzzy Optim Decis Making 2:143–160MathSciNetCrossRefGoogle Scholar
  20. Shen Q, Zhao R, Tang W (2008) Modeling random fuzzy renewal reward processes. IEEE Trans Fuzzy Syst 16:1379–1385CrossRefGoogle Scholar
  21. Yao K, Qin Z (2015) A modified insurance risk process with uncertainty. Insur Math Econ 62:227–233MathSciNetCrossRefzbMATHGoogle Scholar
  22. Zhao R, Tang W, Yun H (2006) Random fuzzy renewal process. Eur J Oper Res 169:189–201MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Faculty of Mathematical SciencesUniversity of GuilanRashtIran
  2. 2.Department of Statistics, Faculty of Mathematical SciencesUniversity of GuilanRashtIran

Personalised recommendations