The Properties Of The Random Walk And Its Applications In Risk Theory

Risk theory, as an important subject of the actuarial mathematics,has been developed for a hundred years;Nowadays, lots of experts have investigated the risk theory by the method of the random walk. In this paper,we will continue to study of the properties of Fandom walks and its applications in the risk theory on the basis of the prodecessor.Chapter I: Suppose{x_k ,k≥1}is a sequence of independent and identically distributed random variables, where their distributions F_k, k≥ 1 are both supported on(-∞,+∞) and F_k ∈S(γ),k≥ 1, Suppose r is a integer-valued random variable,and is independent of {X_k, k≥1 } In this paper, we investigate asymptotic behavior of the tail probabilities P(> x) of the quantities max 0≤ k ≤ nS_k,X_n= max₀≤k≤n X_k and their randomized version S_T,M_T ,X(T) and the local probabilities P( > x) of the quantity S_n,where X₀= 0 by convention and h > 0 is arbitrary fixed.Chapter II: In this chapter , we introduce a non-standard random walk and investigate asymptotic behavior of the tail probabilities P( > x) of the quantitiesChapter III: In this chapter, we introduce two models of random walk, investigate their asymptotic behavior of the tail probabilities of the quantities...