A note on asymptotic behavior for negative drift random walk with dependent heavy-tailed steps and its application to risk theory

作者：Wang Dingcheng^*; Su Chun

来源：Acta Mathematica Scientia, 2007, 27(1): 11-24.

DOI：10.1016/S0252-9602(07)60002-2

• dependent step
• heavy tail
• negative drift random walk
• tail balance condition
• ultimate ruin probability

In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process X-n = -mu+ Sigma(infinity)(j=-infinity) phi(n-j)epsilon(j), where {epsilon, epsilon(n); -infinity < n < +infinity} is a sequence of independent, identically distributed random variables with zero mean, mu > 0 is a constant and the coefficients {phi(i); -infinity < i < infinity} satisfy 0 < Sigma(infinity)(j=-infinity) \j phi j\ < infinity. Under the conditions that the distribution function of \epsilon\ has dominated variation and epsilon satisfies certain tail balance conditions, the asymptotic behavior of P{sup(n >= 0)(-n mu+ Sigma(infinity)(j=-infinity) epsilon(j)beta(nj)) > x} is discussed. Then the result is applied to ultimate ruin probability.

• 出版日期2007-1
• 单位中国科学技术大学; 电子科技大学