Total positivity for cominuscule Grassmannians

In this paper we explore the combinatorics of the non-negative part (G/P)+ of a cominuscule Grassmannian. For each such Grassmannian we define Le-diagrams -- certain fillings of generalized Young diagrams which are in bijection with the cells of (G/P)+. In the classical cases, we describe Le-diagrams explicitly in terms of pattern avoidance. We also define a game on diagrams, by which one can reduce an arbitrary diagram to a Le-diagram. We give enumerative results and relate our Le-diagrams to other combinatorial objects. Surprisingly, the totally non-negative cells in the open Schubert cell of the odd and even orthogonal Grassmannians are (essentially) in bijection with preference functions and atomic preference functions respectively.Comment: 39 page

UK gas markets : the market price of risk and applications to multiple interruptible supply contracts.

We employ the Schwartz and Smith [Schwartz, E., and J. Smith, 2000, Short-term variations and long-term dynamics in commodity prices, Management Science 46, 893–911.] model to explore the dynamics of the UK gasmarkets. We discuss in detail the short-termand long-termmarket prices of risk borne by the market players and how deviations from expected cyclical storage affect the short-term market price of risk. Finally, we illustrate an application of the model by pricing interruptible supply contracts that are currently traded in the UKInterruptible supply contracts; Gas markets; Commodities; Market price of short-term and long-term risk; Multi-exercise Bermudan options; Convenience yield;