We explore negative dependence and stochastic orderings, showing that if an integer-valued random variable W satisfies a certain negative dependence assumption, then W is smaller (in the convex sense) than a Poisson variable of equal mean. Such W include those which may be written as a sum of totally negatively dependent indicators. This is generalised to other stochastic orderings. Application...

Random shifting typically appears in credibility models whereas random scaling is often encountered in stochastic models for claim sizes reflecting the time-value property of money. In this article we discuss some aspects of random shifting and random scaling of insurance risks focusing in particular on credibility models, dependence structure of claim sizes in collective risk models, and extre...

E (1979) showed that inventory costs in a centralized system increase with the correlation between multivariate normal product demands. Using multivariate stochastic orders, we generalize this statement to arbitrary distributions. We then describe methods to construct models with arbitrary dependence structure, using the copula of a multivariate distribution to capture the dependence between th...

We consider the lifetimes of metastable states in bistable evolutionary games (coordination games), and examine how they are affected by spatial structure. A semiclassical approximation based on a path integral method is applied to stochastic evolutionary game dynamics with and without spatial structure, and the lifetimes of the metastable states are evaluated. It is shown that the population d...

Environmental fluctuations often have different impacts on individuals that differ in size, age, or spatial location. To understand how population structure, environmental fluctuations, and density-dependent interactions influence population dynamics, we provide a general theory for persistence for density-dependent matrix models in random environments. For populations with compensating density...

We explore Itô stochastic differential equations where the drift term has possibly infinite dependence on the past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of the coefficients. Uniqueness of the stationary solution is proved if the dependence on the past decays sufficiently fast. The results of this paper ar...

C two markets of different sizes but similar costs and fare structure. All other things being equal, is an airline’s expected revenue larger in the market with larger demand? If not, under what circumstances is it possible to compare expected revenues without carrying out a detailed analysis? In this article, we provide answers to these questions by studying the relationship between the optimal...