Journal of Industrial and Management Optimization (JIMO)

Asymptotics for ruin probabilities in Lévy-driven risk models with heavy-tailed claims
Page number are going to be assigned later 2017

doi:10.3934/jimo.2017044      Abstract        References        Full text (398.9K)      

Yang Yang - Institute of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China (email)
Kam C. Yuen - Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China (email)
Jun-Feng Liu - Institute of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China (email)

1 N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987.
2 Y. Chen and K. W. Ng, The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims, Insurance Math. Econom., 40 (2007), 415-423.
3 Y. Chen, K. W. Ng and Q. Tang, Weighted sums of subexponential random variables and their maxima, Adv. in Appl. Probab., 37 (2005), 510-522.
4 Y. Chen and K. C. Yuen, Sums of pairwise quasi-asymptotically independent random variables with consistent variation, Stoch. Models, 25 (2009), 76-89.
5 D. B. H. Cline and G. Samorodnitsky, Subexponentiality of the product of independent random variables, Stochastic Process. Appl., 49 (1994), 75-98.
6 P. Embrechts, C. Klüppelberg and T. Mikosch, Modelling Extremal Events for Insurance and Finance, Springer-Verlag, Berlin, 1997.
7 S. Foss, D. Korshunov and S. Zachary, An Introduction to Heavy-tailed and Subexponential Distributions, Springer-Verlag, New York, 2011.       
8 A. Frolova, Y. Kabanov and S. Pergamenshchikov, In the insurance business risky investments are dangerous, Finance Stoch., 6 (2002), 227-235.
9 Q. Gao and Y. Wang, Randomly weighted sums with dominated varying-tailed increments and application to risk theory, J. Korean Statist. Society, 39 (2010), 305-314.
10 H. K. Gjessing and J. Paulsen, Present value distributions with applications to ruin theory and stochastic equations, Stochastic Process. Appl., 71 (1997), 123-144.
11 D. R. Grey, Regular variation in the tail behaviour of solutions of random difference equations, Ann. Appl. Probab., 4 (1994), 169-183.
12 F. Guo and D. Wang, Finite- and infinite-time ruin probabilities with general stochastic investment return processes and bivariate upper tail independent and heavy-tailed claims, Adv. in Appl. Probab., 45 (2013), 241-273.
13 X. Hao and Q. Tang, A uniform asymptotic estimate for discounted aggregate claims with sunexponential tails, Insurance Math. Econom., 43 (2008), 116-120.
14 X. Hao and Q. Tang, Asymptotic ruin probabilities for a bivariate Lévy-driven risk model with heavy-tailed claims and risky investments, J. Appl. Probab., 4 (2012), 939-953.
15 C. C. Heyde and D. Wang, Finite-time ruin probability with an exponential Lévy process investment return and heavy-tailed claims, Adv. in Appl. Probab., 41 (2009), 206-224.
16 V. Kalashnikov and D. Konstantinides, Ruin under interest force and subexponential claims: A simple treatment, Insurance Math. Econom., 27 (2000), 145-149.
17 V. Kalashnikov and R. Norberg, Power tailed ruin probabilities in the presence of risky investments, Stochastic Process. Appl., 98 (2002), 211-228.
18 C. Klüppelberg and R. Kostadinova, Integrated insurance risk models with exponential Lévy investment, Insurance Math. Econom., 42 (2008), 560-577.
19 C. Klüppelberg and U. Stadtmüller, Ruin probabilities in the presence of heavy-tails and interest rates, Scand. Actuar. J., 1 (1998), 49-58.
20 D. Konstantinides, Q. Tang and G. Tsitsiashvili, Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails, Insurance Math. Econom., 31 (2002), 447-460.
21 J. Li, Asymptotics in a time-dependent renewal risk model with stochastic return, J. Math. Anal. Appl., 387 (2012), 1009-1023.
22 J. Paulsen, On Cramér-like asymptotics for risk processes with stochastic return on investments, Ann. Appl. Probab., 12 (2002), 1247-1260.
23 J. Paulsen and H. K. Gjessing, Ruin theory with stochastic return on investments, Adv. in Appl. Probab., 29 (1997), 965-985.
24 P. E. Protter, Stochastic Integration and Differential Equations, $2^{nd}$ edition, Springer-Verlag, Berlin, 2003.
25 G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes. Stochastic Models with Infinite Variance, Chapman & Hall, New York, 1994.
26 Q. Tang, The finite-time ruin probability of the compound Poisson model with constant interest force, J. Appl. Probab., 42 (2005), 608-619.
27 Q. Tang, Heavy tails of discounted aggregate claims in the continuous-time renewal model, J. Appl. Probab., 44 (2007), 285-294.
28 Q. Tang and G. Tsitsiashvili, Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks, Stochastic Process. Appl., 108 (2003), 299-325.
29 Q. Tang, G. Wang and K. C. Yuen, Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model, Insurance Math. Econom., 46 (2010), 362-370.
30 Q. Tang and Z. Yuan, Randomly weighted sums of subexponential random variables with application to capital allocation, Extremes, 17 (2014), 467-493.
31 W. Vervaat, On a stochastic difference equation and a representation of nonnegative infinitely divisible random variables, Adv. in Appl. Probab., 11 (1979), 750-783.
32 D. Wang, Finite-time ruin probability with heavy-tailed claims and constant interest rate, Stoch. Models, 24 (2008), 41-57.
33 K. Wang, Y. Wang and Q. Gao, Uniform asymptotics for the finite-time ruin probability of a dependent risk model with a constant interest rate, Methodol. Comput. Appl. Probab., 15 (2013), 109-124.
34 Y. Yang, R. Leipus and J. Šiaulys, On the ruin probability in a dependent discrete time risk model with insurance and financial risks, J. Comput. Appl. Math., 236 (2012), 3286-3295.
35 Y. Yang, J. Lin and Z. Tan, The finite-time ruin probability in the presence of Sarmanov dependent financial and insurance risks, Appl. Math. J. Chinese Univ., 29 (2014), 194-204.
36 Y. Yang, K. Wang and D. Konstantinides, Uniform asymptotics for discounted aggregate claims in dependent risk models, J. Appl. Probab., 51 (2014), 669-684.
37 Y. Yang and Y. Wang, Asymptotics for ruin probability of some negatively dependent risk models with a constant interest rate and dominatedly-varying-tailed claims, Statist. Probab. Letters, 80 (2010), 143-154.

Go to top