| A NOTE ON ASYMPTOTIC BEHAVIOR FOR NEGATIVE DRIFT RANDOM WALK WITH DEPENDENT HEAVY-TAILED STEPS AND ITS APPLICATION TO RISK THEORY |
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| 作者姓名： | 王定成 苏淳 |
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| 作者单位： | School of Applied Mathematics and School of Management University of Electronic Science and Technology of China，Department of Statistics and Finance University of Science and Technology of China Sichuan 610054，China，Anhui 230026，China |
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| 摘 要： | In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process Xn =-μ ∞∑j=-∞ψn-jεj, where {ε, εn; -∞＜ n ＜ ∞}is a sequence of independent, identically distributed random variables with zero mean, μ＞0 is a constant and the coefficients {ψi;-∞＜ i ＜∞} satisfy 0 ＜∞∑j=-∞|jψj| ＜∞. Under the conditions that the distribution function of |ε| has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{supn≥0(-nμ ∞∑j=-∞εjβnj) ＞ x}is discussed. Then the result is applied to ultimate ruin probability.
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| 关 键 词： | 负相漂移 随机游动 非独立步 重尾 风险理论 渐近行为 极限破产概率 |
| 收稿时间： | 2003-03-25 |
| 修稿时间： | 2005-03-11 |
A note on asymptotic behavior for negative drift random walk with dependent heavy-tailed steps and its application to risk theory |
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| Dingcheng Wang,Chun Su,.A NOTE ON ASYMPTOTIC BEHAVIOR FOR NEGATIVE DRIFT RANDOM WALK WITH DEPENDENT HEAVY-TAILED STEPS AND ITS APPLICATION TO RISK THEORY[J].Acta Mathematica Scientia,2007,27(1):11-24. |
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| Authors: | Dingcheng Wang Chun Su |
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| Institution: | aSchool of Applied Mathematics and School of Management, University of Electronic Science and Technology of China, Sichuan 610054, China;bDepartment of Statistics and Finance, University of Science and Technology of China, Anhui 230026, China |
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| Abstract: | In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process where {  , n;-∞< n<+∞} | is a sequence of independent, identically distributed random variables with zero mean, μ > 0 is a constant and the coefficients satisfy Under the conditions that the distribution function of || has dominated variation and satisfies certain tail balance conditions, the asymptotic behavior of is discussed. Then the result is applied to ultimate ruin probability.
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| Keywords: | Dependent step heavy tail negative drift random walk tail balance condition ultimate ruin probability |
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