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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)

A large number n of sensors (finite connected intervals) are placed randomly on the real line so that the distances between the consecutive midpoints are independent random variables with expectation inversely proportional to n. In this work we address two fundamental sensor allocation problems. Interference problem tries to reallocate the sensors from… (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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