Consider a system that consists of several components. Shocks arrive according to a counting process (which may be non-homogeneous and with correlated interarrival times) and each shock may simultaneously destroy a subset of the components. Shock models of this type arise naturally in...

Disruptions and random supplies have been important sources of uncertainty that should be considered in the design and control of supply chains. There have been many real world examples in which a single catastrophic event has simultaneously degraded the capabilities of several suppliers leading...

Tail dependence and conditional tail dependence functions describe, respectively, the tail probabilities and conditional tail probabilities of a copula at various relative scales. The properties as well as the interplay of these two functions are established based upon their homogeneous...

A random vector is said to be of (multivariate) phase-type if it can be represented as the vector of random times until absorptions into various stochastically closed subsets of the finite state space in an absorbing Markov chain. The phase-type distributions are useful since Markovian methods...

One of the most useful tools for handling multivariate distributions with givenunivariatemarginals is the copula function. Using it, any multivariate distribution function can be represented in a way that emphasizes the separate roles of the marginals and of the dependence structure. The goal of...

In this paper we study the first passage time for a damage process to exceed a given threshold or for the maximal increment of this process to pass a certain critical value. Conditions under which this first passage time possesses the NBU, the IFRA or the IFR properties are studied. An...

A distortion risk measure used in finance and insurance is defined as the expected value of potential loss under a scenario probability measure. In this paper, the tail distortion risk measure is introduced to assess tail risks of excess losses modeled by the right tails of loss distributions....

In risk management, ignoring the dependence among various types of claims often results in over-estimating or under-estimating the ruin probabilities of a portfolio. This paper focuses on three commonly used ruin probabilities in multivariate compound risk models, and using the comparison...

The orthant tail dependence describes the relative deviation of upper- (or lower-) orthant tail probabilities of a random vector from similar orthant tail probabilities of a subset of its components, and can be used in the study of dependence among extreme values. Using the conditional approach,...

One of the most useful tools for handling multivariate distributions with givenunivariatemarginals is the copula function. Using it, any multivariate distribution function can be represented in a way that emphasizes the separate roles of the marginals and of the dependence structure. Liet...