東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Backward stochastic differential equ...

Cetin, Coskun.

Linked to FindBook

Google Book

Amazon

博客來

Backward stochastic differential equations with quadratic growth and their applications.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Backward stochastic differential equations with quadratic growth and their applications./
Author:	Cetin, Coskun.
Description:	133 p.
Notes:	Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 6009.
Contained By:	Dissertation Abstracts International66-11B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3196786
ISBN:	9780542425141

Backward stochastic differential equations with quadratic growth and their applications.
Cetin, Coskun.

Backward stochastic differential equations with quadratic growth and their applications. - 133 p.

Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 6009.

Thesis (Ph.D.)--University of Southern California, 2005.

This dissertation discusses backward stochastic differential equations (BSDE's in short) with quadratic growth, their applications to stochastic optimal control problems, and the numerical schemes for the high dimensional cases mainly focusing on linear quadratic regulator (LQR in short) problems.

ISBN: 9780542425141Subjects--Topical Terms:

515831
Mathematics.

Backward stochastic differential equations with quadratic growth and their applications.
LDR:02875nmm 2200313 4500 001 1820448
005 20061113085728.5
008 130610s2005 eng d
020 $a 9780542425141
035 $a (UnM)AAI3196786
035 $a AAI3196786
040 $a UnM $c UnM
100 1 $a Cetin, Coskun. $3 1909672
245 1 0 $a Backward stochastic differential equations with quadratic growth and their applications.
300 $a 133 p.
500 $a Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 6009.
500 $a Adviser: Jaksa Cvitanic.
502 $a Thesis (Ph.D.)--University of Southern California, 2005.
520 $a This dissertation discusses backward stochastic differential equations (BSDE's in short) with quadratic growth, their applications to stochastic optimal control problems, and the numerical schemes for the high dimensional cases mainly focusing on linear quadratic regulator (LQR in short) problems.
520 $a First, we consider the stochastic LQR problem where the state dynamics doesn't depend on the control and the coefficients are deterministic. We characterize a probabilistic representation of the Hamilton-Jacobi-Bellman equation via a decoupled forward-backward SDE (FBSDE) system and discuss the well-posedness of the solutions. By means of an exponential transformation, we obtain the existence-uniqueness of the solutions to this FBSDE system, extend the findings to higher dimensions, give results for the PDE counterparts and provide some comparison theorems. We also consider more general LQR problems which are related to the Riccati BSDE's.
520 $a Next, we discuss the numerical discretization of the decoupled FBSDE's arising from LQR problem relying on the Markov structure of the model and show that this approximation yields a deterministic sequence that converges strongly to the value function of the LQR problem. Then we apply a regression approximation which is based on Malliavin calculus to standard LQR problems in order estimate the conditional expectations involved. We also provide some regularity results and a three dimensional example.
520 $a Finally, we include two applications: An application to economics which is a terminal value modification of an infinite time impulse control of a central bank; and a mean-variance portfolio selection problem which is solved by both LQR approach that is adapted from literature with slight changes and martingale duality method, in a continuous time complete market setting. The dissertation ends with comparing this methods and mentioning other major applications.
590 $a School code: 0208.
650 4 $a Mathematics. $3 515831
650 4 $a Economics, Finance. $3 626650
690 $a 0405
690 $a 0508
710 2 0 $a University of Southern California. $3 700129
773 0 $t Dissertation Abstracts International $g 66-11B.
790 1 0 $a Cvitanic, Jaksa, $e advisor
790 $a 0208
791 $a Ph.D.
792 $a 2005
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3196786