Related papers: On Bellman equation in the limit order optimizatio…
This paper discusses model order reduction of LTI systems over limited frequency intervals within the framework of balanced truncation. Two new \emph{frequency-dependent balanced truncation} methods were developed, one is \emph{SF-type…
In the seminal paper on optimal execution of portfolio transactions, Almgren and Chriss (2001) define the optimal trading strategy to liquidate a fixed volume of a single security under price uncertainty. Yet there exist situations, such as…
We consider a simple model for the evolution of a limit order book in which limit orders of unit size arrive according to independent Poisson processes. The frequencies of buy limit orders below a given price level, respectively sell limit…
We consider a two-way trading problem, where investors buy and sell a stock whose price moves within a certain range. Naturally they want to maximize their profit. Investors can perform up to $k$ trades, where each trade must involve the…
To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by the characteristics of the order flow and…
We present a novel approach to describing the microstructure of high frequency trading using two key elements. First we introduce a new notion of informed trader which we starkly contrast to current informed trader models. We describe the…
We study an optimal execution strategy for purchasing a large block of shares over a fixed time horizon. The execution problem is subject to a general price impact that gradually dissipates due to market resilience. We allow for general…
Market information events are generated intermittently and disseminated at high speeds in real-time. Market participants consume this high-frequency data to build limit order books, representing the current bids and offers for a given…
We model the behavior of three agent classes acting dynamically in a limit order book of a financial asset. Namely, we consider market makers (MM), high-frequency trading (HFT) firms, and institutional brokers (IB). Given a prior dynamic of…
This paper deals with a stochastic order-driven market model with waiting costs, for order books with heterogenous traders. Offer and demand of liquidity drives price formation and traders anticipate future evolutions of the order book. The…
This paper introduces a high frequency trade execution model to evaluate the economic impact of supervised machine learners. Extending the concept of a confusion matrix, we present a 'trade information matrix' to attribute the expected…
This paper examines the role of algorithmic trading in modern financial markets. Additionally, order types, characteristics, and special features of algorithmic trading are described under the lens provided by the large development of high…
We propose an error-correcting model for the microprice, a high-frequency estimator of future prices given higher order information of imbalances in the orderbook. The model takes into account a current microprice estimate given the spread…
We study a an optimal high frequency trading problem within a market microstructure model designed to be a good compromise between accuracy and tractability. The stock price is driven by a Markov Renewal Process (MRP), while market orders…
We study the problem of dynamically trading a futures contract and its underlying asset under a stochastic basis model. The basis evolution is modeled by a stopped scaled Brownian bridge to account for non-convergence of the basis at…
We study semi Lagrangian approximation schemes for Hamilton Jacobi Bellman equations arising from finite horizon optimal control problems. Classical error estimates for these schemes include the term $\frac{1}{\Delta t}$ which leads to…
We exploit cutting-edge deep learning methodologies to explore the predictability of high-frequency Limit Order Book mid-price changes for a heterogeneous set of stocks traded on the NASDAQ exchange. In so doing, we release `LOBFrame', an…
For classification of the high frequency trading quantities, waiting times, price increments within and between sessions are referred to as the a-, b-, and c-increments. Statistics of the a-b-c-increments are computed for the Time & Sales…
The problem of solving Markov decision processes under function approximation remains a fundamental challenge, even under linear function approximation settings. A key difficulty arises from a geometric mismatch: while the Bellman…
This paper poses a few fundamental questions regarding the attributes of the volume profile of a Limit Order Books stochastic structure by taking into consideration aspects of intraday and interday statistical features, the impact of…