123
Views
0
CrossRef citations to date
0
Altmetric
Articles

Lundberg-type inequalities for non-homogeneous risk models

, &
Pages 661-680 | Received 11 Dec 2019, Accepted 09 Oct 2020, Published online: 30 Oct 2020

References

  • Andersen, E. S. On the collective theory of risk in case of contagion between claims. Bull. Inst. Math. Appl. 1957, 12, 275–279.
  • Andrulytė, I. M.; Bernackaitė, E.; Kievinaitė, D.; Šiaulys, J. A Lundberg-type inequality for an inhomogeneous renewal risk model. Mod. Stoch. Theory Appl. 2015, 2, 173–184.
  • Asmussen, S.; Albrecher, H. Ruin Probabilities; World Scientific Publishing: New Jersey, 2010.
  • Asmussen, S.; Rolski, T. Risk theory in a periodic environment: The Cramer-Lundberg approximation and Lundberg’s inequality. Math. Oper. Res. 1994, 19, 410–433. DOI: 10.1287/moor.19.2.410.
  • Bennett, G. Probability inequalities for the sum of independent random variables. J. Am. Stat. Assoc. 1962, 57, 33–45. DOI: 10.1080/01621459.1962.10482149.
  • Bernackaitė, E.; Šiaulys, J. The finite-time ruin probability for an inhomogeneous renewal risk model. J. Ind. Manage. Optim. 2017, 13, 207–222.
  • Björk, T.; Grandell, J. Exponential inequalities for ruin probabilities in the Cox case. Scand. Act. J. 1988, (2), 77–110.
  • Blaževičius, K. Bieliauskienė, E.; Šiaulys, J.; Finite-time ruin probability in the inhomogeneous claim case. Lith. Math. J. 2010, 50, 260–270.
  • Cai, J. Discrete time risk models under rates of interest. Prob. Eng. Inf. Sci. 2002, 16, 309–324. DOI: 10.1017/S0269964802163030.
  • Castañer, A.; Claramunt, M. M.; Gathy, M.; et al. Ruin problems for a discrete time risk model with non-homogeneous conditions. Scand. Act. J. 2013, 2013, 83–102.
  • Cramér, H. On the Mathematical Theory of Risk; Skandia Jubilee: Stockholm, Vol. 4, 1930.
  • Cramér, H. Collective Risk Theory; Skandia Insurance Company: Stockholm, Jubilee Volume, 1955.
  • Dickson, D. C. M. Insurance Risk and Ruin; Cambridge University Press: Cambridge, 2005.
  • Gerber, H. An Introduction to Mathematical Risk Theory; S.S. Huebner Foundation Monographs, University of Pennsylvania: Homewood, 1979.
  • Grandell, J. Aspects of Risk Theory; Springer: New York, 1991.
  • Hoeffding, W. Probability inequalities for sums of bounded random variables. J. Am. Stat. Assoc. 1963, 58, 13–30. DOI: 10.1080/01621459.1963.10500830.
  • Ignatov, Z. G.; Kaishev, V. K. Two-sided bounds for the finite-time probability of ruin. Scand. Act. J. 2000, 2000, 46–62. DOI: 10.1080/034612300750066728.
  • Kievinaitė, D.; Šiaulys, J. Exponential bounds for the tail probability of the supremum of an inhomogeneous random walk. Mod. Stoc. Theory Appl. 2018, 5, 129–143.
  • Kizinevič, E.; Šiaulys, J. The exponential estimate of the ultimate ruin probability for the non-homogeneous renewal risk model. Risks 2018, 6, 20.
  • Lefèvre, C.; Picard, P. A nonhomogeneous risk model for insurance. Comput. Math. Appl. 2006, 51, 325–334.
  • Lundberg, F. Approximerad framställning av sannolikhetsfunktionen. Återförsäkring av kolletivrisker; Acad. Afhaddling. Almqvist. och Wiksell: Uppsala, 1903.
  • Rolski, T.; Schmidli, H.; Schmidt, V.; et al. Stochastic Processes for Insurance and Finance; John Wiley: Chichester, 1998.
  • Răducan, A. M.; Vernic, R.; Zbăganu, G. Recursive calculation of ruin probabilities at or before claim instants for non-identically distributed claims. ASTIN Bull. 2015, 45, 421–443.
  • Răducan, A. M.; Vernic, R.; Zbăganu, G. On the ruin probability for nonhomogeneous claims and arbitrary inter-claim revenues. J. Comput. Appl. Math. 2015, 290, 319–333.
  • Tuncel, A.; Tank, F. Computational results on the compound binomial risk model with nonhomogeneous claim occurrences. J. Comput. Appl. Math. 2014, 263, 69–77. DOI: 10.1016/j.cam.2013.12.004.
  • Wang, H. X.; Fang, D. F.; Tang, M. N. Ruin probabilities under a Markovian risk model. Acta Math. Appl. Sin. 2003, 19, 621–630. DOI: 10.1007/210255-003-0136-9.
  • Yang, H. Non-exponential bounds for ruin probability with interest effect included. Scand. Act. J. 1999, 1999, 66–79. DOI: 10.1080/03461230050131885.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.