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THE ULTIMATE RUIN PROBABILITY OF A DEPENDENT DELAYED-CLAIM RISK MODEL PERTURBED BY DIFFUSION WITH CONSTANT FORCE OF INTEREST

Qingwu Gao|Erli Zhang|Na Jin
대한수학회 (The Korean Mathematical Society)|2015.05|대한수학회보 (Bulletin of the KMS)|제52권 제3호|pp. 895-906

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참고문헌

키워드

diffusionasymptotic ruin probabilitydelayed claimpairwise quasi-asymptotic independencewidely lower orthant dependence
주제분류수학

초록

Recently, Li [12] gave an asymptotic formula for the ultimate ruin probability in a delayed-claim risk model with constant force of interest and pairwise quasi-asymptotically independent and extendedregularly- varying-tailed claims. This paper extends Li’s result to the case in which the risk model is perturbed by diffusion, the claims are consistently-varying-tailed and the main-claim interarrival times are widely lower orthant dependent.

Abstract

Recently, Li [12] gave an asymptotic formula for the ultimate ruin probability in a delayed-claim risk model with constant force of interest and pairwise quasi-asymptotically independent and extendedregularly- varying-tailed claims. This paper extends Li’s result to the case in which the risk model is perturbed by diffusion, the claims are consistently-varying-tailed and the main-claim interarrival times are widely lower orthant dependent.

참고문헌 (28)

  1. N. H. Bingham, "Regular Variation" (1987), Cambridge University Press
  2. Y. Chen, "Sums of pairwise quasi-asymptotically independent random variables with consistent variation", Stoch. Models, 25(1), pp.76~89 (2009)
  3. D. B. H. Cline, "Subexponentiality of the product of independent random variables", Stochastic Process. Appl, 49(1), pp.75~98 (1994)
  4. P. Embrechts, "Modelling Extremal Events for Insur-ance and Finance" (1997), Springer
  5. Qingwu Gao, "ASYMPTOTIC RUIN PROBABILITIES IN A GENERALIZED JUMP-DIFFUSION RISK MODEL WITH CONSTANT FORCE OF INTEREST", 대한수학회지, 51(4), pp.735~749 (2014), 대한수학회
  6. Q. Gao, "Randomly weighted sums of pairwise quasi upper-tail independent increments with application to risk theory", Comm. Statist. Theory Methods (2015)[DOI]
  7. Q. Gao, "Asymptotic behavior of the finite-time ruin probability with pairwise quasi-asymptotically independent claims and constant interest force", Rocky Mountain J. Math, 44(5), pp.1505~1528 (2014)
  8. Q. Gao, "Uniform asymptotics for the finite-time ruin probability with upper tail asymptotically independent claims and constant force of interest", Statist. Probab. Lett, 83(6), pp.1527~1538 (2013)
  9. Q. Gao, "Asymptotic ruin probabilities in a generalized bidimensional risk model perturbed by diffusion with constant force of interest", J. Math. Anal. Appl, 419(2), pp.1193~1213 (2014)
  10. Qingwu Gao, "Uniform asymptotics for the finite-time ruin probability in a general risk model with pairwise quasi-asymptotically independent claims and constant interest force", 대한수학회보, 50(2), pp.611~626 (2013), 대한수학회
  11. J. Geluk, "Asymptotic tail probabilities of sums of dependent subexponential random variables", J. Theoret. Probab, 22(4), pp.871~882 (2009)
  12. J. Li, "On pairwise quasi-asymptotically independent random variables and their appli-cations", Statist. Probab. Lett, 83(9), pp.2081~2087 (2013)
  13. J. Li, "The Gerber-Shiu discounted penalty function for a compound binomial risk model with by-claims", Acta Math. Appl. Sin. Engl. Ser, 31(1), pp.181~190 (2015)
  14. X. Liu, "A note on a dependent risk model with constant interest rate", Statist. Probab. Lett, 82(4), pp.707~712 (2012)
  15. H. Meng, "On the expected discounted penalty function in a delayed-claims risk model", Acta Math. Appl. Sin. Engl. Ser, 28(2), pp.215~224 (2012)
  16. Q. Tang, "Asymptotic ruin probabilities of the renewal model with constant interest force and regular variation", Scand. Actuar. J, 2005(1), pp.1~5 (2005)
  17. Q. Tang, "Precise estimates for the ruin probability in finite hori-zon in a discrete-time model with heavy-tailed insurance and financial risks", Stochastic Process. Appl, 108(2), pp.299~325 (2003)
  18. Q. Tang, "Randomly weighted sums of subexponential random variables with application to ruin theory", Extremes, 6(3), pp.171~188 (2003)
  19. D. Wang, "Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory", Sci. China Ser. A, 48(10), pp.1379~1394 (2005)
  20. K. Wang, "Uniform asymptotics for the finite-time ruin probabil-ity of a dependent risk model with a constant interest rate", Methodol. Comput. Appl. Probab, 15(1), pp.109~124 (2013)
  21. Y. Wang, "Basic renewal theorems for a random walk with widely de-pendent increments and their applications", J. Math. Anal. Appl, 384(2), pp.597~606 (2011)
  22. H. R. Waters, "Ruin probabilities allowing for delay in claims settlement", Insurance Math. Econom, 4(2), pp.113~122 (1985)
  23. Y. Xiao, "The compound binomial risk model with time-correlated claims", Insurance Math. Econom, 41(1), pp.124~133 (2007)
  24. H. Xie, "Expected present value of total dividends in a delayed claims risk model under stochastic interest rates", Insurance Math. Econom, 46(2), pp.415~422 (2010)
  25. H. Xie, "On the expected discounted penalty function for the compound Poisson risk model with delayed claims", J. Comput. Appl. Math, 235(8), pp.2392~2404 (2011)
  26. K. C. Yuen, "Ruin probabilities for time-correlated claims in the compound binomial model", Insurance Math. Econom, 29(1), pp.47~57 (2001)
  27. K. C. Yuen, "On ultimate ruin in a delayed-claims risk model", J. Appl. Probab, 42(1), pp.163~174 (2005)
  28. Wei Zou, "On the probability of ruin in a continuous risk model with delayed claims", 대한수학회지, 50(1), pp.111~125 (2013), 대한수학회

관련 논문AI추천

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