In this article, a special case of two coupled M/G/1-queues is considered, where two servers are exposed to two types of jobs that are distributed among the servers via a random switch. In this model, the asymptotic behavior of the workload buffer exceedance probabilities for the two single...

In general, risk of an extreme outcome in financial markets can be expressed as a function of the tail copula of a high-dimensional vector after standardizing marginals. Hence it is of importance to model and estimate tail copulas. Even for moderate dimension, nonparametrically estimating a tail...

The estimation of P(S-n u) by simulation, where S, is the sum of independent. identically distributed random varibles Y-1,..., Y-n, is of importance in many applications. We propose two simulation estimators based upon the identity P(S-n u) = nP(S, u, M-n = Y-n), where M-n = max(Y-1,...,...

Stock returns exhibit heavy tails and volatility clustering. These features, motivating the use of GARCH models, make it difficult to predict times and sizes of losses that might occur. Estimation of losses, like the Value-at-Risk, often assume that returns, normalized by the level of...

In insurance, if the insurer continuously invests her wealth in risk-free and risky assets, then the price process of the investment portfolio can be described as a geometric Lévy process. People always are interested in estimating the tail distribution of the stochastic present value of...

Asymptotic results are obtained for several conditional measures of association. The chosen random variables are the first two order statistics and the total sum within a random sum. Many of the results have confirmed the “one-jump” property of the risk model. Non-trivial limits are...

We establish a “Central Limit Theorem” for rank distributions, which provides a detailed characterization and classification of their universal macroscopic statistics and phase transitions. The limit theorem is based on the statistical notion of Lorenz curves, and is termed the “Lorenzian...

The mode-coupling equations used to study glasses and supercooled liquids define the underlying regenerative processes represented by an indicator function Z(t). Such a process is a special case of an alternating renewal process, and it introduces in a natural way a stochastic two level system....

Consider the linear nonhomogeneous fixed-point equation R=D∑i=1NCiRi+Q, where (Q,N,C1,C2,…) is a random vector with N∈{0,1,2,3,…}∪{∞},Ci≥0 for all i∈N, P(|Q|0)0, and {Ri}i∈N is a sequence of i.i.d. random variables independent of (Q,N,C1,C2,…) having the same distribution as...