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34
Limit Order Book as a Market for Liquidity
, 2001
"... We develop a dynamic model of an orderdriven market populated by discretionary liquidity traders. These traders must trade, yet can choose the type of order and are fully strategic in their decision. Traders differ by their impatience: less patient traders demand liquidity, more patient traders p ..."
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Cited by 96 (7 self)
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We develop a dynamic model of an orderdriven market populated by discretionary liquidity traders. These traders must trade, yet can choose the type of order and are fully strategic in their decision. Traders differ by their impatience: less patient traders demand liquidity, more patient traders provide it. Three equilibrium patterns are obtained the pattern is determined by three parameters: the degree of impatience of the patient traders, which we model as the cost of execution delay in providing liquidity; their proportion in the population, which determines the degree of competition among the liquidity providers; and the tick size, which is the cost of the minimal price improvement. Despite its simplicity, the model generates a rich set of empirical predictions on the relation between market parameters, time to execution, and spreads. We argue that the economic intuition of this model is so basic, its Limit and market orders constitute the core of any orderdriven continuous trading
A dynamic model of the limit order book
 Review of Financial Studies
"... I propose a continuoustime model of price formation in a market where trading is conducted according to a limitorder book. Strategic liquidity traders arrive randomly in the market and dynamically choose between limit and market orders, trading off execution price with waiting costs. I prove the e ..."
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Cited by 51 (0 self)
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I propose a continuoustime model of price formation in a market where trading is conducted according to a limitorder book. Strategic liquidity traders arrive randomly in the market and dynamically choose between limit and market orders, trading off execution price with waiting costs. I prove the existence of a Markov equilibrium in which the bid and ask prices depend only on the numbers of buy and sell orders in the book, and which can be characterized in closedform in several cases of interest. My model generates empirically verified implications for the shape of the limitorder book and the dynamics of prices and trades. In particular, I show that buy and sell orders can cluster away from the bidask spread, thus generating a humpshaped limitorder book. Also, following a market buy order, both the ask and bid prices increase, with the ask increasing more than the bid—hence the spread widens.
Statistical theory of the continuous double auction. Quantitative Finance 3
"... Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this paper we develop a microscopic dynamical statistical model for the continuous double auction under the assumption of IID random order flow, and analyse it using simulatio ..."
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Cited by 49 (5 self)
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Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this paper we develop a microscopic dynamical statistical model for the continuous double auction under the assumption of IID random order flow, and analyse it using simulation, dimensional analysis, and theoretical tools based on mean field approximations. The model makes testable predictions for basic properties of markets, such as price volatility, the depth of stored supply and demand versus price, the bid–ask spread, the price impact function, and the time and probability of filling orders. These predictions are based on properties of order flow and the limit order book, such as share volume of market and limit orders, cancellations, typical order size, and tick size. Because these quantities can all be measured directly there are no free parameters. We show that the order size, which can be cast as a nondimensional granularity parameter, is in most cases a more significant determinant of market behaviour than tick size. We also provide an explanation for the observed highly concave nature of the price impact function. On a broader level, this work suggests how stochastic models based on zero intelligence agents may be useful to probe the structure of market institutions. Like the model of perfect rationality, a stochastic zero intelligence model can be used to make strong predictions based on a compact set of assumptions, even if these assumptions are not fully believable. 1.
Surrogate Gradient Algorithm for Lagrangian Relaxation
 Journal of Optimization Theory and Applications
, 1999
"... The subgradient method is frequently used to optimize dual functions in Lagrangian relaxation for separable integer programming problems. In the method, all subproblems must be optimally solved to obtain a subgradient direction. In this paper, the "surrogate subgradient method" is develope ..."
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Cited by 46 (21 self)
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The subgradient method is frequently used to optimize dual functions in Lagrangian relaxation for separable integer programming problems. In the method, all subproblems must be optimally solved to obtain a subgradient direction. In this paper, the "surrogate subgradient method" is developed, where a proper direction can be obtained without optimally solving all the subproblems. In fact, only approximate optimization of one subproblem is needed to get a proper "surrogate subgradient direction," and the directions are smooth for problems of large size. The convergence of the algorithm is proved. Compared with methods that take effort to find better directions, this method can obtain good directions with much less effort, and provides a new approach that is especially powerful for problems of very large size.
Competition among trading venues: Information and trading on electronic communications networks
 Journal of Finance
, 2003
"... This paper explores the competition between two trading venues, Electronic Communication Networks (ECNs) and Nasdaq market makers. ECNs o¡er the advantages of anonymity and speed of execution, which attract informed traders. Thus, trades are more likely to occur on ECNs when information asymmetry is ..."
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Cited by 36 (4 self)
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This paper explores the competition between two trading venues, Electronic Communication Networks (ECNs) and Nasdaq market makers. ECNs o¡er the advantages of anonymity and speed of execution, which attract informed traders. Thus, trades are more likely to occur on ECNs when information asymmetry is greater and when trading volume and stockreturn volatility are high. ECN trades have greater permanent price impacts and more private information is revealed through ECN trades than though marketmaker trades. However, ECN trades have higher ex ante trading costs because market makers can preference or internalize the less informed trades and o¡er them better executions. TECHNOLOGICAL INNOVATIONS THAT ENABLE HIGHSPEED, lowcost electronic trading systems are dramatically changing the structure of ¢nancial markets. Exchanges and markets around the world are merging or forming alliances to improve liquidity and reduce costs in the face of increased competition from each other and from these computerized trading systems.Trading volume on Electronic Communications Networks (ECNs) has grown rapidly over the past several years. ECNs are now involved in more than a third of Nasdaq trading volume and are attempting to increase their market share in NYSElisted
padic reconstruction of rational numbers
 ACM SIGSAM Bulletin
, 1982
"... In a recent paper, Wang [1981] introduces a padic algorithm for the construction of partial fraction decompositions. This differs from the usual padic algorithms for factorisation or the computation of ..."
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Cited by 24 (0 self)
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In a recent paper, Wang [1981] introduces a padic algorithm for the construction of partial fraction decompositions. This differs from the usual padic algorithms for factorisation or the computation of
Unit Completion for a Computeraided Translation System
 Machine Translation
, 2000
"... This work is in the context of TRANSTYPE, a system that observes its user as he or she types a translation and repeatedly suggests completions for the text already entered. The user may either accept, modify, or ignore these suggestions. We describe the design, implementation, and performance of a p ..."
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Cited by 20 (5 self)
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This work is in the context of TRANSTYPE, a system that observes its user as he or she types a translation and repeatedly suggests completions for the text already entered. The user may either accept, modify, or ignore these suggestions. We describe the design, implementation, and performance of a pro totype which suggests completions of units of texts that are longer than one word.
Sparse Hensel lifting
 In EUROCAL 85 European Conf. Comput. Algebra Proc
, 1985
"... Anew algorithm is introduced which computes the multivariate leading coefficients of polynomial factors from their univariate images. This algorithm is incorporated into a sparse Hensel lifting scheme and only requires the factorization of a single univariate image. The algorithm also provides the c ..."
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Cited by 17 (6 self)
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Anew algorithm is introduced which computes the multivariate leading coefficients of polynomial factors from their univariate images. This algorithm is incorporated into a sparse Hensel lifting scheme and only requires the factorization of a single univariate image. The algorithm also provides the content of the input polynomial in the main variable as a byproduct. We show how we can take advantage of this property when computing the GCD of multivariate polynomials by sparse Hensel lifting. 1.
Correction of Disfluencies in Spontaneous Speech using a NoisyChannel Approach
 in Proceedings of the 8th Eurospeech Conference
, 2003
"... In this paper we present a system which automatically corrects disfluencies such as repairs and restarts typically occurring in spontaneously spoken speech. The system is based on a noisychannel model and its development requires no linguistic knowledge, but only annotated texts. Therefore, it has ..."
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Cited by 12 (3 self)
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In this paper we present a system which automatically corrects disfluencies such as repairs and restarts typically occurring in spontaneously spoken speech. The system is based on a noisychannel model and its development requires no linguistic knowledge, but only annotated texts. Therefore, it has large potential for rapid deployment and the adaptation to new target languages. The experiments were conducted on spontaneously spoken dialogs from the English VERBMOBIL corpus where a recall of 77.2% and a precision of 90.2% was obtained. To demonstrate the feasibility of rapid adaptation additional experiments on the spontaneous Mandarin Chinese CallHome corpus were performed achieving 49.4% recall and 76.8% precision.