Acta mathematica scientia,Series B

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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

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

CLC Number: 

  • 62N01
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