Extended Abstract. The simplest and the most common way of comparing two random variables is through their means and variances. It may happen that in some cases the median of X is larger than that of Y, while the mean of X is smaller than the mean of Y. However, this confusion will not arise if the random variables are stochastically ordered. Similarly, the same may happen if one would like to ...

We consider a rich tanker trailer routing problem with stochastic transit times for chemicals and liquid bulk orders. A typical route of the tanker trailer comprises of sourcing a cleaned and prepped trailer from a pre-wash location, pickup and delivery of chemical orders, cleaning the tanker trailer at a post-wash location after order delivery and prepping for the next order. Unlike traditiona...

We consider a dynamic reinsurance market, where the traded risk process is driven by a jump-diffusion and where claim amounts are unbounded. These markets are known to be incomplete, and there are typically infinitely many martingale measures. In this case, no-arbitrage pricing theory can typically only provide wide bounds on prices of reinsurance claims. Optimal martingale measures such as the...

Random variables may be compared with respect to their location by comparing certain functionals ad hoc, such as the mean or median, or by means of stochastic ordering based directly on the properties of the corresponding distribution functions. These alternative approaches are brought together in this paper. We focus on the class of L-functionals discussed by Bickel and Lehmann (1975) and char...

In this paper, we study stochastic orders of scalar products of random vectors. Based on the study of Ma (2000), we first obtain more general conditions under which linear combinations of random variables can be ordered in the increasing convex order. As an application of this result, we consider the scalar product of two random vectors which separates the severity effect and the frequency effe...

The present paper aims to point out how the stationary-excess operator and its iterates transform the s-convex stochastic orders and the associated moment spaces. This allows us to propose a new unified method on constructing s-convex extrema for distributions that are known to be t-monotone. Both discrete and continuous cases are investigated. Several extremal distributions under monotonicity ...