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Expansion of a Filtration with a Sto...

Neufcourt, Leo.

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Expansion of a Filtration with a Stochastic Process A High-Frequency Trading Perspective.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Expansion of a Filtration with a Stochastic Process A High-Frequency Trading Perspective./
作者:	Neufcourt, Leo.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2017,
面頁冊數:	154 p.
附註:	Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
Contained By:	Dissertation Abstracts International79-02B(E).
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10691046
ISBN:	9780355408362

Expansion of a Filtration with a Stochastic Process A High-Frequency Trading Perspective.
Neufcourt, Leo.

Expansion of a Filtration with a Stochastic Process A High-Frequency Trading Perspective. - Ann Arbor : ProQuest Dissertations & Theses, 2017 - 154 p.

Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.

Thesis (Ph.D.)--Columbia University, 2017.

This item is not available from ProQuest Dissertations & Theses.

A theory of expansion of filtrations has been developed since the 1970s to model dynamic probabilistic problems with asymmetric information. It has found a special echo in mathematical finance around the concept of insider trading, which has appeared in return very convenient for expressing the abstract properties of augmentations of filtrations. Research has historically focused on two particular classes of expansions, initial and progressive expansions, corresponding to additional information generated respectively by a random variable and a random time. Although they can reproduce some stylized facts in the insider trading paradigm, those two types of expansions are too restrictive to model quantitatively dynamic phenomenons of contemporary interest such as the topical high-frequency trading. In order to model such a continuous flow of information Kchia and Protter (2015) introduce augmentations of filtrations where the additional information is generated by a stochastic process.

ISBN: 9780355408362Subjects--Topical Terms:

517247
Statistics.

Expansion of a Filtration with a Stochastic Process A High-Frequency Trading Perspective.
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520 $a A theory of expansion of filtrations has been developed since the 1970s to model dynamic probabilistic problems with asymmetric information. It has found a special echo in mathematical finance around the concept of insider trading, which has appeared in return very convenient for expressing the abstract properties of augmentations of filtrations. Research has historically focused on two particular classes of expansions, initial and progressive expansions, corresponding to additional information generated respectively by a random variable and a random time. Although they can reproduce some stylized facts in the insider trading paradigm, those two types of expansions are too restrictive to model quantitatively dynamic phenomenons of contemporary interest such as the topical high-frequency trading. In order to model such a continuous flow of information Kchia and Protter (2015) introduce augmentations of filtrations where the additional information is generated by a stochastic process.
520 $a This thesis complements the pioneering work of Kchia and Protter (2015) with an analysis of the information drift appearing in the transformation of semimartingales, which leads to a quantitative valuation of the additional information. In the preliminary chapters we introduce the general framework of expansions of filtrations and present the information drift as a key proxy to the value of information by characterizing its existence as a no-arbitrage condition and expressing problems the value increase of optimization problems associated with additional information as one of its integrals. The theoretical core of this thesis is formed by two series of convergence theorems for semimartingales and their information drifts under a new topology on filtrations, from which we derive the transformation of semimartingales when the filtration is augmented with a stochastic process as well as a computational method to estimate the information drift. We finally study several dynamical examples of anticipative expansions of a Brownian filtration with stochastic processes, where the information drift does or does not exist, and set the foundations for an ongoing application to estimating the advantage of high-frequency traders on the general market.
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