國立虎尾科技大學 |

Geometry and Optimization of Relative Arbitrage.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Geometry and Optimization of Relative Arbitrage./
作者:	Wong, Ting Kam Leonard.
面頁冊數:	1 online resource (189 pages)
附註:	Source: Dissertation Abstracts International, Volume: 77-11(E), Section: B.
Contained By:	Dissertation Abstracts International77-11B(E).
標題:	Mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9781339940946

Geometry and Optimization of Relative Arbitrage.
Wong, Ting Kam Leonard.

Geometry and Optimization of Relative Arbitrage. - 1 online resource (189 pages)

Source: Dissertation Abstracts International, Volume: 77-11(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

This thesis is devoted to the mathematics of volatility harvesting, the idea that extra portfolio growth may be created by systematic rebalancing. First developed by E. R. Fernholz in the late 90s and the early 2000s, stochastic portfolio theory provides a novel mathematical framework to analyze this phenomenon. A major result of the theory is the construction of portfolio strategies that outperform the market portfolio under realistic conditions. These portfolios are called relative arbitrage opportunities.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781339940946Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Geometry and Optimization of Relative Arbitrage.
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100 1 $a Wong, Ting Kam Leonard. $3 1179078
245 1 0 $a Geometry and Optimization of Relative Arbitrage.
264 0 $c 2016
300 $a 1 online resource (189 pages)
336 $a text $b txt $2 rdacontent
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338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 77-11(E), Section: B.
500 $a Adviser: Soumik Pal.
502 $a Thesis (Ph.D.) $c University of Washington $d 2016.
504 $a Includes bibliographical references
520 $a This thesis is devoted to the mathematics of volatility harvesting, the idea that extra portfolio growth may be created by systematic rebalancing. First developed by E. R. Fernholz in the late 90s and the early 2000s, stochastic portfolio theory provides a novel mathematical framework to analyze this phenomenon. A major result of the theory is the construction of portfolio strategies that outperform the market portfolio under realistic conditions. These portfolios are called relative arbitrage opportunities.
520 $a In this thesis we adopt a discrete time, pathwise approach which reveals deep connections with optimal transport, nonparametric statistics and information geometry. Our main object of study is functionally generated portfolio, a family of volatility harvesting investment strategies with remarkable properties.
520 $a This thesis consists of three parts. Part I gives a convex-analytic treatment of functionally generated portfolio and relates it with optimal transport theory. The optimal transport point of view provides the geometric structure required in order that a portfolio map is volatility harvesting.
520 $a Part II turns to optimization of functionally generated portfolio. We introduce an optimization problem analogous to shape-constrained maximum likelihood density estimation. The Bayesian version of this problem leads naturally to an extension of T. M. Cover's universal portfolio and large deviations.
520 $a Finally, in Part III we introduce and study the information geometry of exponentially concave functions, a deep and elegant geometric framework underlying the ideas of Part I. It extends the dually flat geometry of Bregman divergence studied by S. Amari and others, leading to plenty of problems for further study.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Finance. $3 559073
650 4 $a Statistics. $3 556824
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0508
690 $a 0463
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of Washington. $b Mathematics. $3 1179079
773 0 $t Dissertation Abstracts International $g 77-11B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10138537 $z click for full text (PQDT)