In this handout we review results concerning representation of partial orders via stochastic orders and investigate their applications to some classes of stochastic dominance conditions applied in inequality, poverty and welfare measurement. The results obtained in an unidimensional framework are extended to multidimensional analysis. In particular we provide an overview of the main issues conc...

Abstract: In this article the problem of optimal trading in illiquid markets is addressed when the deviations from a given stochastic target function describing, for instance, external aggregate client flow are penalised. Using techniques of singular stochastic control, we extend the results of [NW11] to a two-sided limit order market with temporary market impact and resilience, where the bid a...

In this paper we consider sufficient conditions in order to stochastically compare random vectors of multivariate mixture models. In particular we consider stochastic and convex orders, the likelihood ratio order, and the hazard rate and mean residual life dynamic orders. Applications to proportional hazard models and mixture models in risk theory are also given. AMS Subject Classification: 60E...

We consider two important time scales—the Markov and cryptic orders—that monitor how an observer synchronizes to a finitary stochastic process. We show how to compute these orders exactly and that they are most efficiently calculated from the -machine, a process’s minimal unifilar model. Surprisingly, though the Markov order is a basic concept from stochastic process theory, it is not a probabi...

We consider two important time scales-the Markov and cryptic orders-that monitor how an observer synchronizes to a finitary stochastic process. We show how to compute these orders exactly and that they are most efficiently calculated from the ε-machine, a process's minimal unifilar model. Surprisingly, though the Markov order is a basic concept from stochastic process theory, it is not a probab...

In this article we give theoretical results for different stochastic orders of a log-scale-location family which uses Tsallis statistics functions. These describe the inequalities moments or Gini index according to parameters. We also compute mean in case q-Weibull and q-Gaussian distributions. The paper is aimed at analyzing order between survival functions, Lorenz curves (as consequences) tog...

The rounding of orders to achieve a batch size is recognised as a source of the bullwhip problem within supply chains. While it is often advocated that batch sizes should be reduced as much as possible, there has been limited investigation into the impact of batching on bullwhip. Here we consider scenarios where orders are placed only in multiples of a fixed batch size, for both deterministic a...

We model an environment where orders arrive probabilistically over time, with their revenues and capacity requirements becoming known upon arrival. The decision is whether to accept an order, receiving a reward and reserving capacity, or reject an order, freeing capacity for possible future arrivals. We model the dynamic, stochastic multiple knapsack problem (DSMKP) with stochastic dynamic prog...