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Limits of Limit-Order Books
Trading of financial instruments has largely moved away from floor trading and onto electronic exchanges. Orders to buy and sell are queued at these...
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Order Execution Probability and Order Queue in Limit Order Markets
The sha** of a limit order book illustrates the dynamics of the trading process, the changing pattern of the execution probability of limit orders...
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The Book
Paul Erdös liked to speak of “The Book,” which was where God had recorded the most elegant mathematical proofs. In 1985, he said, “You don’t have to...
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Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models
We analyse an optimal trade execution problem in a financial market with stochastic liquidity. To this end, we set up a limit order book model in...
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Equilibrium Model of Limit Order Books: A Mean-Field Game View
In this paper, we propose a continuous time equilibrium model of the (sellside) limit order book (LOB) in which the liquidity dynamics follows a...
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Entire solutions of higher order differential equations with entire coefficients having the same order
In this paper, we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order,...
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Chapter 1 Centers and Limit Cycles
In this chapter I want to give a general background to the center-focus problem, and then to show why the problem is interesting: both in what it...
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Semiclassical Analysis in the Limit Circle Case
We consider second order differential equations with real coefficients that are in the limit circle case at infinity. Using the semiclassical Ansatz,...
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Maximum Estimates for Solutions to Elliptic and Parabolic Equations on a Book-Type Stratified Set
Studying PDEs on the sets of complicated structure and, in particular, stratified sets has been gaining popularity since recently. This article...
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Limit Cycles of Continuous Piecewise Smooth Differential Systems
From the beginning of this century many articles have been published on the continuous and discontinuous piecewise differential systems specially in...
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Scaling Limit for the Peeling Process
In this chapter, we describe the scaling limit for the evolution of the perimeter and volume processes during filled-in explorations under...
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Richter’s local limit theorem, its refinement, and related results*
We give a detailed exposition of the proof of Richter’s local limit theorem in a refined form and establish the stability of the remainder term in...
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Via Order Markets Towards Price-Taking Equilibrium
Can order markets lead participants towards price-taking equilibrium ? Viewing market sessions as steps of iterative algorithms, this paper indicates...
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On the Weak Second-order Optimality Condition for Nonlinear Semidefinite and Second-order Cone Programming
Second-order necessary optimality conditions for nonlinear conic programming problems that depend on a single Lagrange multiplier are usually built...
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Levy’s continuity theorem and central limit theorem
This chapter explores the use of characteristic functions in probability theory. The characteristic function of a random variable contains all the...
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The self-financing equation in limit order book markets
The goal of this paper is to present a mathematical framework for trading on a limit order book, including its associated transaction costs, and to...
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Thermodynamic Game and the Kac Limit in Quantum Lattices
A mathematically rigorous computation of the pressure and equilibrium states of important short-range quantum models on lattices (like the Hubbard...
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On the existence of supporting broken book decompositions for contact forms in dimension 3
We prove that in dimension 3 every nondegenerate contact form is carried by a broken book decomposition. As an application we obtain that on a closed...
