The authors investigate the tail probability of the supremum of a random walk with independent increments and obtain some equivalent assertions in the case that the increments are independent and identically distributed random variables with Osubexponential integrated distributions.A uniform upper bound is derived for the distribution of the supremum of a random walk with independent but non-identically distributed increments,whose tail distributions are dominated by a common tail distribution with an O-subexponential integrated distribution.
Let {Y i;∞ < i < ∞} be a doubly infinite sequence of identically distributed-mixing random variables and let {a i;∞ < i < ∞} be an absolutely summable sequence of real numbers.In this paper we study the moments of sup(1 ≤ r < 2,p > 0) under the conditions of some moments.
Consider a discrete-time insurance risk modelWithin period i, i ≥ 1, Xi and Yi denote the net insurance loss and the stochastic discount factor of an insurer, respectively.Assume that {(Xi, Yi), i ≥ 1} form a sequence of independent and identically distributed random vectors following a common bivariate Sarmanov distributionIn the presence of heavy-tailed net insurance losses, an asymptotic formula is derived for the finite-time ruin probability.
