In this paper, we consider the strong stability of a type of Jamison weighted sums, which not only extend the corresponding result of Jamison etc. [13] from i.i.d. case to END random variables, but also obtain the necessary and sufficient results. As an important consequence, we present the result of SLLN as that of i.i.d. case.

<p style='text-indent:20px;'>This paper studies ruin probabilities of a generalized bidimensional risk model with dependent and heavy-tailed claims and additional net loss processes. When the claim sizes have long-tailed and dominated-varying-tailed distributions, precise asymptotic formulae for two kinds of finite-time ruin probabilities are derived, where the two claim-number processes from different lines of business are almost arbitrarily dependent. Under some extra conditions on the independence relation of claim inter-arrival times, the class of the claim-size distributions is extended to the subexponential distribution class. In order to verify the accuracy of the obtained theoretical result, a simulation study is performed via the crude Monte Carlo method.</p>

In this paper, we focus on a bidimensional risk model with heavy-tailed claims and geometric L?vy price processes, in which the two claim-number processes generated by the two kinds of business are not necessary to be identical and can be arbitrarily dependent. In this model, the claim size vectors (X1,Y1), (X2,Y2),... are supposed to be independent and identically distributed random vectors, but for i ? 1, each pair (Xi,Yi) follows the strongly asymptotic independence structure. Under the assumption that the claims have consistently varying tails, an asymptotic formula for the infinite-time ruin probability is established, which extends the existing results in the literature to some extent.

No abstract

No abstract