Asymptotics for the partial sum and its maximum of dependent random variables*

Zhang, Ting; Xi-nian, Fang; Liu, Jie; Yang, Yang

doi:10.1007/s10986-017-9348-1

Cited by 2 publications

(2 citation statements)

References 23 publications

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“…The results of the present paper are complementary to those obtained by Albrecher et al [1], Ambagaspitiya [2], Bernackaitė and Šiaulys [5,6], Castañer et al [7], Cojocaru [9], Constantinescu et al [10], Czarna and Palmowski [11], Damarackas and Šiaulys [12], Danilenko et al [13], Grigutis et al [17,18], Jordanova and Stehlík [20], Mishura et al [24], Rȃducan et al [26][27][28], Ragulina [29], Zhang et al [33], Zhang et al [34] and other authors who dealt with different inhomogeneous risk models.…”

Section: The Ultimate Ruin Probabilitysupporting

confidence: 87%

Exponential bounds for the tail probability of the supremum of an inhomogeneous random walk

Kievinaitė¹,

Šiaulys²

2018

Modern Stochastics: Theory and Applications

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Let {ξ 1 , ξ 2 , . . .} be a sequence of independent but not necessarily identically distributed random variables. In this paper, the sufficient conditions are found under which the tail probability P(sup n 0 n i=1 ξ i > x) can be bounded above by 1 exp{− 2 x} with some positive constants 1 and 2 . A way to calculate these two constants is presented. The application of the derived bound is discussed and a Lundberg-type inequality is obtained for the ultimate ruin probability in the inhomogeneous renewal risk model satisfying the net profit condition on average.

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