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• W2951492718 endingPage "1350025" @default.
• W2951492718 startingPage "1350025" @default.
• W2951492718 abstract "Motivated by the desire to bridge the gap between the microscopic description of price formation (agent-based modeling) and the stochastic differential equations approach used classically to describe price evolution at macroscopic time scales, we present a mathematical study of the order book as a multidimensional continuous-time Markov chain and derive several mathematical results in the case of independent Poissonian arrival times. In particular, we show that the cancellation structure is an important factor ensuring the existence of a stationary distribution and the exponential convergence towards it. We also prove, by means of the functional central limit theorem (FCLT), that the rescaled-centered price process converges to a Brownian motion. We illustrate the analysis with numerical simulation and comparison against market data." @default.
• W2951492718 created "2019-06-27" @default.
• W2951492718 creator A5021381756 @default.
• W2951492718 creator A5057979561 @default.
• W2951492718 date "2013-07-25" @default.
• W2951492718 modified "2023-09-25" @default.
• W2951492718 title "A MATHEMATICAL APPROACH TO ORDER BOOK MODELING" @default.
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• W2951492718 doi "https://doi.org/10.1142/s0219024913500258" @default.
• W2951492718 hasPublicationYear "2013" @default.
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