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We construct an optimal execution strategy for the purchase of a large number of shares of a financial asset over a fixed interval of time. Purchases of the asset have a nonlinear impact on price, and this is moderated over time by resilience in the limit-order book that determines the price. The limit-order book is permitted to have arbitrary shape. The… (More)

—We consider a problem of supplying electricity to a set of N customers in a smart-grid framework. Each customer requires a certain amount of electrical energy which has to be supplied during the time interval [0, 1]. We assume that each demand has to be supplied without interruption, with possible duration between and r, which are given system parameters… (More)

—We consider a problem of supplying electricity to a network of electric demands, N , in a smart-grid framework. Each demand requires a random amount of electrical energy which has to be supplied during the time interval [0, 1]. We model this network by malleable rectangular shape demands, and then relate the resulted scheduling problem to well known Strip… (More)

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