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Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate

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Abstract

This paper gives an asymptotically equivalent formula for the finite-time ruin probability of a nonstandard risk model with a constant interest rate, in which both claim sizes and inter-arrival times follow a certain dependence structure. This new dependence structure allows the underlying random variables to be either positively or negatively dependent. The obtained asymptotics hold uniformly in a finite time interval. Especially, in the renewal risk model the uniform asymptotics of the finite-time ruin probability for all times have been given. The obtained results have extended and improved some corresponding results.

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References

  • Bingham NH, Goldie CM, Teugels JM (1987) Regular variation. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Block HW, Savits TH, Shaked M (1982) Some concepts of negative dependence. Ann Probab 10:765–772

    Article  MathSciNet  MATH  Google Scholar 

  • Chen Y, Ng KW (2007) The ruin probability of the renewal model with constant interest force and negatively dependent heavy-tailed claims. Insur Math Econ 40:415–423

    Article  MathSciNet  MATH  Google Scholar 

  • Cline DBH, Samorodnitsky G (1994) Subexponentiality of the product of independent random variables. Stoch Process Their Appl 49:75–98

    Article  MathSciNet  MATH  Google Scholar 

  • Denisov D, Foss S, Korshunov D (2004) Tail asymptotics for the supremum of a random walk when the mean is not finite. Queueing Syst 46:15–33

    Article  MathSciNet  MATH  Google Scholar 

  • Ebrahimi N, Ghosh M (1981) Multivariate negative dependence. Commun Stat 10:307–337

    Article  MathSciNet  Google Scholar 

  • Embrechts P, Klüppelberg C, Mikosch T (1997) Modelling extremal events for insurance and finance. Springer, Berlin

    Book  MATH  Google Scholar 

  • Hao X, Tang Q (2008) A uniform asymptotic estimate for discounted aggregate claims with sunexponential tails. Insur Math Econ 43:116–120

    Article  MathSciNet  MATH  Google Scholar 

  • Kalashnikov V, Konstantinides D (2000) Ruin under interest force and subexponential claims: a simple treatment. Insur Math Econ 27:145–149

    Article  MathSciNet  MATH  Google Scholar 

  • Klüppelberg C (1988) Subexponential distributions and integrated tails. J Appl Probab 25:132–141

    Article  MathSciNet  MATH  Google Scholar 

  • Klüppelberg C, Stadtimuller U (1998) Ruin probability in the presence of heavy-tails and interest rates. Scand Actuar J 1998(1):49–58

    Article  MATH  Google Scholar 

  • Kong F, Zong G (2008) The finite-time ruin probability for ND claims with constant interest force. Stat Probab Lett 78:3103–3109

    Article  MathSciNet  MATH  Google Scholar 

  • Konstantinides D, Tang Q, Tsitsiashvili G (2002) Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails. Insur Math Econ 31:447–460

    Article  MathSciNet  MATH  Google Scholar 

  • Korshunov D (2002) Large-deviation probabilities for maxima of sums of independent random variables with negaive mean and subexponential distribution. Theory Probab Appl 46:355–366

    Article  MathSciNet  Google Scholar 

  • Lehmann EL (1966) Some concepts of dependence. Ann Math Stat 37:1137–1153

    Article  MATH  Google Scholar 

  • Li J, Wang K, Wang Y (2009) Finite-time ruin probability with NQD dominated varying-tailed claims and NLOD inter-arrival times. J Syst Sci Complex 22:407–414

    Article  MathSciNet  MATH  Google Scholar 

  • Liu L (2009) Precise large deviations for dependent random variables with heavy tails. Stat Probab Lett 79:1290–1298

    Article  MATH  Google Scholar 

  • Nelsen RB (2006) An introduction to Copulas, 2nd edn. Springer, New York

    MATH  Google Scholar 

  • Tang Q (2004) Asymptotics for the finite time ruin probability in the renewal model with consistent variation. Stoch Models 20:281–297

    Article  MathSciNet  MATH  Google Scholar 

  • Tang Q (2005a) Asymptotic ruin probabilities of the renewal model with constant interest force and regular variation. Scand Actuar J 2005(1):1–5

    Article  MATH  Google Scholar 

  • Tang Q (2005b) The finite-time ruin probability of the compound Poisson model with constant interest force. J Appl Probab 42:608-619

    Article  MathSciNet  MATH  Google Scholar 

  • Tang Q (2007) Heavy tails of discounted aggregrate claims in the continuous-time renewal model. J Appl Probab 44:285–294

    Article  MathSciNet  MATH  Google Scholar 

  • Tang Q, Tsitsiashvili G (2003) Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks. Stoch Process Their Appl 108:299–325

    MathSciNet  MATH  Google Scholar 

  • Wang D (2008) Finite-time ruin probability with heavy-tailed claims and constant interest rate. Stoch Models 24:41–57

    Article  MathSciNet  MATH  Google Scholar 

  • Wang Y, Cui Z, Wang K, Ma X (2009) Uniform asymptotics of the finite-time ruin probability with NLOD inter-occurrence times. (submitted)

  • Yang Y, Wang Y (2010) Asymptotics for ruin probability of some nagatively dependent risk models with a constant interest rate and dominatedly-varying-tailed claims. Stat Probab Lett 80:143–154

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics, Soochow University, Suzhou, 215006, People’s Republic of China

    Kaiyong Wang, Yuebao Wang & Qingwu Gao

  2. School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou, 215009, People’s Republic of China

    Kaiyong Wang

  3. School of Mathematics and Statistics, Nanjing Audit University, Nanjing, 211815, People’s Republic of China

    Qingwu Gao

Authors
  1. Kaiyong Wang
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  2. Yuebao Wang
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  3. Qingwu Gao
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Corresponding author

Correspondence to Yuebao Wang.

Additional information

This work was supported by National Science Foundation of China (NO. 10671139, 11071182), Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 10KJB110010) and the research foundation of SUST.

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Wang, K., Wang, Y. & Gao, Q. Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate. Methodol Comput Appl Probab 15, 109–124 (2013). https://doi.org/10.1007/s11009-011-9226-y

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  • DOI: https://doi.org/10.1007/s11009-011-9226-y

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