Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Continuity problem for singular BSDE with random terminal time
Download
index.pdf
Date
2022-1-01
Author
Samuel, Sharoy Augustine
Popier, Alexandre
Sezer, Ali Devin
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
127
views
80
downloads
Cite This
All Rights Reserved.We study a class of non-linear Backward stochastic differential equations (BSDE) with a superlinear driver process f adapted to a filtration F and over a random time interval [[0, S]] where S is a stopping time of F. The terminal condition ξ is allowed to take the value +∞, i.e., singular. We call a stopping time S solvable with respect to a given BSDE and filtration if the BSDE has a minimal supersolution with terminal value 1 at terminal time S. Our goal is to show existence of solutions to the BSDE for a range of singular terminal values under the assumption that S is solvable. We will do so by proving that the minimal supersolution to the BSDE is a solution, i.e., it is continuous at time S and attains the terminal value with probability 1. We consider three types of terminal values: 1) Markovian: i.e., ξ is of the form ξ = g(ΞS) where Ξ is a continuous Markovian diffusion process, S is a hitting time of Ξ and g is a deterministic function 2) terminal conditions of the form (Formula Presented) and 3) (Formula Presented) where Ƭ is another stopping time. For general ξ we prove that minimal supersolution has a limit at time S provided that F is left continuous at time S. Finally, we discuss the implications of our results about Markovian terminal conditions to the solution of non-linear elliptic PDE with singular boundary conditions
Subject Keywords
Backward stochastic differential equation
,
stopping time
,
singularity
,
continuity problem
,
POSITIVE SOLUTIONS
,
DIFFERENTIAL-EQUATIONS
,
TERMINAL CONDITION
,
BOUNDARY
,
TRACE
,
JUMPS
,
Backward stochastic differential equation
,
Continuity problem
,
Singularity
,
Stopping time
URI
https://hdl.handle.net/11511/101830
Journal
Alea (Rio de Janeiro)
DOI
https://doi.org/10.30757/alea.v19-49
Collections
Graduate School of Applied Mathematics, Article
Suggestions
OpenMETU
Core
Continuity problem for backward stochastic differential equations with singular nonmarkovian terminal conditions and deterministic terminal times
Ahmadi, Mahdi; Sezer, Ali Devin; Department of Financial Mathematics (2020-9)
In this thesis we study a class of Backward Stochastic Differential Equations (BSDE) with superlinear driver process f adapted to a filtration F = fFt; t 2 [0; T]g supporting at least a d dimensional Brownian motion and a Poisson random measure on Rm n f0g in a deterministic time interval [0; T]. The superlinearity of f allows terminal conditions that can take the value +1 with positive probability. Such terminal conditions are called “singular.” A terminal condition is said to be Markovian if it is a det...
Backward stochastic differential equations and Feynman-Kac formula in the presence of jump processes
İncegül Yücetürk, Cansu; Yolcu Okur, Yeliz; Hayfavi, Azize; Department of Financial Mathematics (2013)
Backward Stochastic Differential Equations (BSDEs) appear as a new class of stochastic differential equations, with a given value at the terminal time T. The application area of the BSDEs is conceptually wide which is known only for forty years. In financial mathematics, El Karoui, Peng and Quenez have a fundamental and significant article called “Backward Stochastic Differential Equations in Finance” (1997) which is taken as a groundwork for this thesis. In this thesis we follow the following steps: Firstl...
Continuity problem for backward stochastic differential equations with singular nonmarkovian terminal conditions and random terminal times
Samuel, Sharoy Augustine; Sezer, Ali Devin; Department of Financial Mathematics (2021-7)
We study a class of nonlinear BSDEs with a superlinear driver process f adapted to a filtration F and over a random time interval [0, S] where S is a stopping time of F. The filtration is assumed to support at least a d-dimensional Brownian motion as well as a Poisson random measure. The terminal condition ξ is allowed to take the value +∞, i.e., singular. Our goal is to show existence of solutions to the BSDE in this setting. We will do so by proving that the minimal supersolution to the BSDE is a so luti...
Boundary value problems for higher order linear impulsive differential equations
Uğur, Ömür; Akhmet, Marat (2006-07-01)
In this paper higher order linear impulsive differential equations with fixed moments of impulses subject to linear boundary conditions are studied. Green's formula is defined for piecewise differentiable functions. Properties of Green's functions for higher order impulsive boundary value problems are introduced. An appropriate example of the Green's function for a boundary value problem is provided. Furthermore, eigenvalue problems and basic properties of eigensolutions are considered. (c) 2006 Elsevier In...
Least squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of convection-diffusion problems
Bozkaya, Canan (2005-03-18)
The least squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of the dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in convection-diffusion type problems. The DRBEM enables us to use the fundamental solution of the Laplace equation which is easy to implement computationally. The time derivative and the convection terms are considered as the nonhomogeneity in the equation which are ap...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
S. A. Samuel, A. Popier, and A. D. Sezer, “Continuity problem for singular BSDE with random terminal time,”
Alea (Rio de Janeiro)
, vol. 19, no. 2, pp. 1185–1220, 2022, Accessed: 00, 2023. [Online]. Available: https://hdl.handle.net/11511/101830.