Backward stochastic differential equations with non-markovian singular terminal conditions for general driver and filtration

Date

2021-01-01

Author

Ahmadi, Mahdi
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

136
views

0
downloads

All rights reserved.We consider a class of Backward Stochastic Differential Equations with superlinear driver process f adapted to a filtration supporting at least a d dimensional Brownian motion and a Poisson random measure on Rm \ {0}. We consider the following class of terminal conditions: ξ1 = ∞ · 1{τ1≤T } where τ1 is any stopping time with a bounded density in a neighborhood of T and ξ2 = ∞ · 1AT where At, t ∈ [0, T ] is a decreasing sequence of events adapted to the filtration Ft that is continuous in probability at T (equivalently, AT = {τ2 > T } where τ2 is any stopping time such that P(τ2 = T) = 0). In this setting we prove that the minimal supersolutions of the BSDE are in fact solutions, i.e., they attain almost surely their terminal values. We note that the first exit time from a time varying domain of a d-dimensional diffusion process driven by the Brownian motion with strongly elliptic covariance matrix does have a continuous density. Therefore such exit times can be used as τ1 and τ2 to define the terminal conditions ξ1 and ξ2. The proof of existence of the density is based on the classical Green’s functions for the associated PDE.

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85109099827&origin=inward
https://hdl.handle.net/11511/91373

Journal

Electronic Journal of Probability

DOI

https://doi.org/10.1214/21-ejp619

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

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...
Least-squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of diffusive-convective problems Bozkaya, Canan (Elsevier BV, 2007-01-01) Least-squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in diffusive-convective type problems with variable coefficients. The DRBEM enables us to use the fundamental solution of Laplace equation, which is easy to implement computation ally. The terms except the Laplacian are considered as the nonhomogeneity in the equation, which ar...
Continuity problem for singular BSDE with random terminal time Samuel, Sharoy Augustine; Popier, Alexandre; Sezer, Ali Devin (2022-1-01) 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 solutio...
EXACT BOUND STATES OF THE D-DIMENSIONAL KLEIN-GORDON EQUATION WITH EQUAL SCALAR AND VECTOR RING-SHAPED PSEUDOHARMONIC POTENTIAL IKHDAİR, SAMEER; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2008-09-01) We present the exact solution of the Klein Gordon equation in D-dimensions in the presence of the equal scalar and vector pseudoharmonic potential plus the ring-shaped potential using the Nikiforov-Uvarov method. We obtain the exact bound state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this ring-shaped pseudoharmonic potential can be reduced to the three-dimensional (3D) pseudoharmonic solution once the coupling constant of the angular ...
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

M. Ahmadi, A. Popier, and A. D. Sezer, “Backward stochastic differential equations with non-markovian singular terminal conditions for general driver and filtration,” Electronic Journal of Probability, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85109099827&origin=inward.