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Expansion of Filtrations with Stochastic Processes in the Perspective of High-Frequency Trading | Hanlon Financial Systems Center

Expansion of Filtrations with Stochastic Processes in the Perspective of High-Frequency Trading

Expansion of Filtrations with Stochastic Processes in the Perspective of High-Frequency Trading

Event Location: 
BC 122
Event Time: 
Thursday, April 6, 2017 - 5:00pm to 6:00pm

Leo Neufcourt

PhD Student - Statistics, Columbia University

ABSTRACT: We will consider a financial market where an insider agent has access to some additional information which has the form of a general stochastic process. In the perspective of high-frequency trading we can think of a process describing the shape of the limit order book or the evolution of the price. In a general semimartingale framework, if the market without insider is free of arbitrage, absence of arbitrage of opportunities for the insider is closely related to the existence of a semimartingale decomposition for the price in the augmented filtration, in which the finite variation term admits a density with respect to the quadratic variation of the semimartingale, the information drift. The information drift is also fundamental to understand the advantage of the insider in absence of arbitrage opportunities and its L2 norm provides a quantitative measure of the statistical advantage of the insider. The classical cases of initial and progressive expansions are well understood via Jacod’s condition. We extend Jacod’s condition to expansions with a process using approximations with discrete samples, and show that a uniform L2 bound on the finite variation terms implies conservation of semimartingales, absence of arbitrage and finite additional logarithmic utility for an insider. This is a joint work with Philip Protter.

 

BIO:  Leo Neufcourt is a finishing PhD student in Statistics at Columbia. His research has focused on stochastic processes and mathematical finance. He particularly studied expansion of filtrations, discrete Gaussian processes and volatility models published several articles in major journals. Currently a Dean’s fellow at Columbia, Leo is also an alumni from Ecole Polytechnique. He has been a visitor at Universidad de Valparaiso, Universidad de Chile, Chinese University of Hong Kong and Université Paris VI. He has also worked as a quantitative analyst at BNP Paribas and Zeliade Systems and been a consultant for financial companies.