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Reflected Anticipated Backward Stochastic Differential Equations with Default Risk, Numerical Algorithms and Applications

  • This thesis consists of two parts, i.e. the theoretical background of (R)ABSDE including basic theorems, theoretical proofs and properties (Chapter 2-4), as well as numerical algorithms and simulations for (R)ABSDES (Chapter 5). For the theoretical part, we study ABSDEs (Chapter 2), RABSDEs with one obstacle (Chapter 3)and RABSDEs with two obstacles (Chapter 4) in the defaultable setting respectively, including the existence and uniqueness theorems, applications, the comparison theorem for ABSDEs, their relations with PDEs and stochastic differential delay equations (SDDE). The numerical algorithm part (Chapter 5) introduces two main algorithms, a discrete penalization scheme and a discrete reflected scheme based on a random walk approximation of the Brownian motion as well as a discrete approximation of the default martingale; we give the convergence results of the algorithms, provide a numerical example and an application in American game options in order to illustrate the performance of the algorithms.

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Author:Jingnan WangORCiD
URN (permanent link):urn:nbn:de:hbz:386-kluedo-62960
DOI:https://doi.org/10.26204/KLUEDO/6296
Advisor:Ralf Korn
Document Type:Doctoral Thesis
Language of publication:English
Publication Date:2021/03/12
Year of Publication:2021
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2020/11/20
Date of the Publication (Server):2021/03/12
Number of page:XIII, 137
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65]
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)