数学物理学报(英文版)

• 论文 • 上一篇    下一篇

A NOTE ON ASYMPTOTIC BEHAVIOR FOR NEGATIVE DRIFT RANDOM WALK WITH DEPENDENT HEAVY-TAILED STEPS AND ITS APPLICATION TO RISK THEORY

王定成; 苏淳   

  1. 中国科技大学统计与金融系, 合肥 230026
  • 收稿日期:2003-03-25 修回日期:2005-03-11 出版日期:2007-01-20 发布日期:2007-01-20
  • 通讯作者: 苏淳
  • 基金资助:

    Research supported by National Science Foundation of China (70671018 and 10371117)

A NOTE ON ASYMPTOTIC BEHAVIOR FOR NEGATIVE DRIFT RANDOM WALK WITH DEPENDENT HEAVY-TAILED STEPS AND ITS APPLICATION TO RISK THEORY

Wang Dingcheng; Su Chun   

  1. Department of Statistics and Finance, University of Science and Technology of China, Anhui 230026, China
  • Received:2003-03-25 Revised:2005-03-11 Online:2007-01-20 Published:2007-01-20
  • Contact: Su Chun

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=-∞arphin-jεj, where {ε,εn ;-∞0 is a constant and the coefficients {\varphii; -∞<i<∞} satisfy 0<∑j=-∞|j arphij | <∞. Under conditions the distribution function of |ε| has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{supn≥0( -n μ +∑j=-∞εjβnj)> x } is discussed. Then the result is applied to ultimate ruin probability.

关键词: Dependent step, heavy tail, negative drift random walk, tail balance condition, ultimate ruin probability

Abstract:

In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process Xn=-μ +∑j=-∞arphin-jεj, where {ε,εn ;-∞0 is a constant and the coefficients {\varphii; -∞<i<∞} satisfy 0<∑j=-∞|j arphij | <∞. Under conditions the distribution function of |ε| has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{supn≥0( -n μ +∑j=-∞εjβnj)> x } is discussed. Then the result is applied to ultimate ruin probability.

Key words: Dependent step, heavy tail, negative drift random walk, tail balance condition, ultimate ruin probability

中图分类号: 

  • 62N01