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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 41, Fasc. 2,
pages 217 - 235
DOI: 10.37190/0208-4147.41.2.2
Published online 2.9.2021
 

Exponential bounds of ruin probabilities for non-homogeneous risk models

Qianqian Zhou
Alexander Sakhanenko
Junyi Guo

Abstract:

Lundberg-type inequalities for ruin probabilities of non-homogeneous risk models are presented. By employing the martingale method, upper bounds of ruin probabilities are obtained for general risk models under weak assumptions. In addition, several risk models, including the newly defined united risk model and a quasi-periodic risk model with interest rate, are studied.

2010 AMS Mathematics Subject Classification: Primary 91G05; Secondary 60K10.

Keywords and phrases: non-homogeneous risk model, martingale method, ruin probability, Lundberg-type inequality.

I. M. Andrulytå, E. Bernackaitå, D. Kievinaitå and J. Šiaulys, A Lundberg-type inequality for an inhomogeneous renewal risk model, Modern Stoch. Theory Appl. 2 (2015), 173-184.

S. Asmussen and H. Albrecher, Ruin Probabilities, World Sci., 2010.

S. Asmussen and T. Rolski, Risk theory in a periodic environment: the Cramer-Lundberg approximation and Lundberg's inequality, Math. Oper. Res. 19 (1994), 410-433.

L. Bai and J. Guo, Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint, Insurance Math. Econom. 42 (2008), 968-975.

G. Bennett, Probability inequalities for the sum of independent random variables, J. Amer. Statist. Assoc. 57 (1962), 33–45.

E. Bernackaitå and J. Šiaulys, The finite-time ruin probability for an inhomogeneous renewal risk model, J. Industrial Management Optim. 13 (2017), 207-222.

K. Blaževičius, E. Bieliauskienå and J. Šiaulys, Finite-time ruin probability in the inhomogeneous claim case, Lithuanian Math. J. 50 (2010), pp.260-270.

A. Castañer, M. M. Claramunt, M. Gathy, C. Lefèvre and M. Marmol, Ruin problems for a discrete time risk model with non-homogeneous conditions, Scand. Actuar. J. 2013, 83-102.

H. Cramér, On the mathematical theory of risk, in: Skandia Jubilee Vol. 2, Stockholm, 1930, 7-84.

H. Cramér, Collective risk theory, Jubilee Volume, Skandia Insurance Company, 1955.

D. C. M. Dickson, Insurance Risk and Ruin, Cambridge Univ. Press, 2005.

H. Gerber, An Introduction to Mathematical Risk Theory, Univ. of Pennsylvania, 1979.

J. Grandell, Aspects of Risk Theory, Springer, New York, 1991.

W. Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Statist. Assoc. 58 (1963), 13-30.

Z. G. Ignatov and V. K. Kaishev, Two-sided bounds for the finite-time probability of ruin, Scand. Actuar. J. 2000, 46-62.

D. Kievinaitå and J. Šiaulys, Exponential bounds for the tail probability of the supremum of an inhomogeneous random walk, Modern Stoch. Theory Appl. 5 (2018), pp.129-143.

J. F. C. Kingman, Poisson Processes, Clarendon Press, Oxford, 1993.

E. Kizinevič and J. Šiaulys, The exponential estimate of the ultimate ruin probability for the non-homogeneous renewal risk model, Risks 6 (2018), 17 pp.

C. Lefèvre and P. Picard, A nonhomogeneous risk model for insurance, Computers Math. Appl. 51 (2006), 325-334.

F. Lundberg, Approximations of the probability function. Reinsurance of collective risks, Acad. Afhaddling, Almqvist och Wiksell, Uppsala, 1903 (in Swedish).

J. Paulsen, Present value of some insurance portfolios, Scand. Actuar. J. 1997, 11-37.

T. Rolski, H. Schmidli, V. Schmidt and J. L. Teugels, Stochastic Processes for Insurance and Finance, Wiley, Chichester, 1998.

H. Schmidli, Stochastic Control in Insurance, Springer, London, 2007.

A. Tuncel and F. Tank, Computational results on the compound binomial risk model with nonhomogeneous claim occurrences, J. Comput. Appl. Math. 263 (2014), 69-77.

R. Vernic, On a conjecture related to the ruin probability for nonhomogeneous insurance claims, An. Stiint. Univ. Ovidius Constanta Ser. Mat. 23 (2015), 209-220.

Q. Q. Zhou, A. Sakhanenko and J. Y. Guo, Lundberg-type inequalities for non-homogeneous risk models, Stoch. Models 36 (2020), 661-680.

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