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Dynamic conic finance via backward s...

Chen, Tao.

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Dynamic conic finance via backward stochastic difference equations and recursive construction of confidence regions.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Dynamic conic finance via backward stochastic difference equations and recursive construction of confidence regions./
Author:	Chen, Tao.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
Description:	150 p.
Notes:	Source: Dissertation Abstracts International, Volume: 78-03(E), Section: B.
Contained By:	Dissertation Abstracts International78-03B(E).
Subject:	Applied mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10174176
ISBN:	9781369287028

Dynamic conic finance via backward stochastic difference equations and recursive construction of confidence regions.
Chen, Tao.

Dynamic conic finance via backward stochastic difference equations and recursive construction of confidence regions. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 150 p.

Source: Dissertation Abstracts International, Volume: 78-03(E), Section: B.

Thesis (Ph.D.)--Illinois Institute of Technology, 2016.

This thesis consists of two major parts, and it contributes to the fields of mathematical finance and statistics.

ISBN: 9781369287028Subjects--Topical Terms:

2122814
Applied mathematics.

Dynamic conic finance via backward stochastic difference equations and recursive construction of confidence regions.
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100 1 $a Chen, Tao. $3 3235352
245 1 0 $a Dynamic conic finance via backward stochastic difference equations and recursive construction of confidence regions.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2016
300 $a 150 p.
500 $a Source: Dissertation Abstracts International, Volume: 78-03(E), Section: B.
500 $a Advisers: Tomasz R. Bielecki; Igor Cialenco.
502 $a Thesis (Ph.D.)--Illinois Institute of Technology, 2016.
520 $a This thesis consists of two major parts, and it contributes to the fields of mathematical finance and statistics.
520 $a The contribution to mathematical finance is made via developing new theoretical results in the area of conic finance. Specifically, we have advanced dynamic aspects of conic finance by developing an arbitrage free theoretical framework for modeling bid and ask prices of dividend paying securities using the theory of dynamic acceptability indices. This has been done within the framework of general probability spaces and discrete time. In the process, we have advanced the theory of dynamic sub-scale invariant performance measures. In particular, we proved a representation theorem of such measures in terms of a family of dynamic convex risk measures, and provided a representation of dynamic risk measures in terms of BSDeltaEs.
520 $a The contribution to statistics is of fundamental importance as it initiates the theory underlying recursive computation of confidence regions for finite dimensional parameters in the context of stochastic dynamical systems. In the field of engineering, particularly in the field of control engineering, the area of recursive point estimation came to great prominence in the last forty years. However, there has been no work done with regard to recursive computation of confidence regions. To partially fill this gap, the second part of the thesis is devoted to recursive construction of confidence regions for parameters characterizing the one-step transition kernel of a time-homogeneous Markov chain.
590 $a School code: 0091.
650 4 $a Applied mathematics. $3 2122814
650 4 $a Statistics. $3 517247
650 4 $a Finance. $3 542899
690 $a 0364
690 $a 0463
690 $a 0508
710 2 $a Illinois Institute of Technology. $b Applied Mathematics. $3 3195037
773 0 $t Dissertation Abstracts International $g 78-03B(E).
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791 $a Ph.D.
792 $a 2016
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10174176