Academic Journal
Numerical methods and their analyses for backward Stochastic differential equations
| Title: | Numerical methods and their analyses for backward Stochastic differential equations |
|---|---|
| Contributors: | Zhang, Yufei (author.), Zou, Jun , 1962- (thesis advisor.), Chinese University of Hong Kong Graduate School. Division of Mathematics. (degree granting institution.) |
| Publication Year: | 2017 |
| Collection: | The Chinese University of Hong Kong: CUHK Digital Repository / 香港中文大學數碼典藏 |
| Subject Terms: | Stochastic differential equations--Numerical solutions, Stochastic processes, QA274.23 .Z63 2017eb |
| Description: | M.Phil. ; Backward stochastic differential equations (BSDEs) have attracted considerable attention due to their wide applications in mathematical finance and stochastic control. As it is usually difficult to obtain analytic solutions of BSDEs, it is of paramount importance to construct efficient and robust numerical methods for BSDEs. ; This thesis focuses on the numerical resolutions of BSDEs and contains two parts. In the first one, we shall propose several numerical schemes for forwardbackward stochastic differential equations (FBSDEs) based on a new fundamental concept of transposition solutions. These schemes exploit time-splitting methods for the variation of constants formula of the associated partial differential equations and a discrete representation of the transition semigroups. The convergence of the schemes is established for FBSDEs with uniformly Lipschitz drivers, locally Lipschitz and maximal monotone drivers. Numerical experiments are presented for several nonlinear financial derivative pricing problems to demonstrate the adaptivity and effectiveness of the new schemes. The ideas can be applied to construct high-order schemes for FBSDEs with general Markov forward processes. ; The second part of the thesis is devoted to the derivations of semi-analytic solutions to some nonlinear BSDEs. We shall first propose several numerical schemes for BSDEs based on an explicit Itô representation of the terminal conditions. These schemes replace the required computations of conditional expectations in most existing schemes with a direct truncation of coefficients, and consequently greatly reduce the computational costs. We shall further demonstrate that these schemes allow us deriving semi-analytic solutions with only time discretization of some basic nonlinear BSDEs, which provides us with a new approach to construct analytic solutions of some nonlinear BSDEs. ; 近年來，倒向隨機微分方程引起了廣泛的關注，這主要歸功於這類方程在數理金融和隨機控制領域的大量應用。由於構造一般倒向隨機微分方程的解析解是十分困難的, 設計高效穩健的數值解法變得尤為重要。 ... |
| Document Type: | text |
| File Description: | electronic resource; remote; 1 online resource (82 leaves) : illustrations (some color); computer; online resource |
| Language: | English Chinese |
| Availability: | https://julac.hosted.exlibrisgroup.com/primo-explore/search?query=addsrcrid,exact,991039531367003407,AND&tab=default_tab&search_scope=All&vid=CUHK&mode=advanced&lang=en_US https://repository.lib.cuhk.edu.hk/en/item/cuhk-1839481 |
| Rights: | Use of this resource is governed by the terms and conditions of the Creative Commons "Attribution-NonCommercial-NoDerivatives 4.0 International" License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
| Accession Number: | edsbas.803CE8BD |
| Database: | BASE |
| Description not available. |