Related papers: Ergodicity and diffusivity of Markovian order book…
Robust Markov Decision Processes (MDPs) are a powerful framework for modeling sequential decision-making problems with model uncertainty. This paper proposes the first first-order framework for solving robust MDPs. Our algorithm interleaves…
In this paper, we introduce a parametrized family of prices derived from the Maximum Entropy Principle. The price is obtained from the distribution that minimizes bias, given the bid and ask volume imbalance at the top of the order book.…
We address the problem of executing large client orders in continuous double-auction markets under time and liquidity constraints. We propose a model predictive control (MPC) framework that balances three competing objectives: order…
In this paper we consider a Bayesian framework for making inferences about dynamical systems from ergodic observations. The proposed Bayesian procedure is based on the Gibbs posterior, a decision theoretic generalization of standard…
We propose a structural framework for the geometry of financial order books in which liquidity, supply, and demand are treated as emergent observables rather than primitive economic variables. The market is modeled as an inflationary…
We consider a continuous-review inventory system in which the setup cost of each order is a general function of the order quantity and the demand process is modeled as a Brownian motion with a positive drift. Assuming the holding and…
When modelling stock market dynamics, the price formation is often based on an equilbrium mechanism. In real stock exchanges, however, the price formation is goverend by the order book. It is thus interesting to check if the resulting…
Buying and selling stocks causes price changes, which are described by the price impact function. To explain the shape of this function, we study the Island ECN orderbook. In addition to transaction data, the orderbook contains information…
We conduct modeling of the price dynamics following order flow imbalance in market microstructure and apply the model to the analysis of Chinese CSI 300 Index Futures. There are three findings. The first is that the order flow imbalance is…
We study a model of the motion by mean curvature of an (1+1) dimensional interface in a 2D Brownian velocity field. For the well-posedness of the model we prove existence and uniqueness for certain degenerate nonlinear stochastic evolution…
Quasi-equilibrium models for aggregate variables are widely-used throughout finance and economics. The validity of such models depends crucially upon assuming that the systems' participants behave both independently and in a Markovian…
Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…
We show that multivariate Hawkes processes coupled with the nonparametric estimation procedure first proposed in Bacry and Muzy (2015) can be successfully used to study complex interactions between the time of arrival of orders and their…
In this work, we aim to reconcile several apparently contradictory observations in market microstructure: is the famous "square-root law" of metaorder impact, which decays with time, compatible with the random-walk nature of prices and the…
This thesis develops a new framework for modelling price processes in finance, such as an equity price or foreign exchange rate. This can be related to the conventional Ito calculus-based framework through the time integral of a price's…
We present a methodology for representing probabilistic relationships in a general-equilibrium economic model. Specifically, we define a precise mapping from a Bayesian network with binary nodes to a market price system where consumers and…
In this paper, we consider an infinite horizon, continuous-review, stochastic inventory system in which cumulative customers' demand is price-dependent and is modeled as a Brownian motion. Excess demand is backlogged. The revenue is earned…
Devising models of the limit order book that realistically reproduce the market response to exogenous trades is extremely challenging and fundamental in order to test trading strategies. We propose a novel explainable model for small tick…
We investigate the behavior of limit order books on the meso-scale motivated by order execution scheduling algorithms. To do so we carry out empirical analysis of the order flows from market and limit order submissions, aggregated from…
Dynamic pricing is the practice of adjusting the selling price of a product to maximize a firm's revenue by responding to market demand. The literature typically distinguishes between two settings: infinite inventory, where the firm has…