scholarly journals Generalized BSDE driven by a Lévy process

2006 ◽  
Vol 2006 ◽  
pp. 1-25 ◽  
Author(s):  
Mohamed El Otmani
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equation ◽  
Existence Of A Solution ◽  
One Dimensional ◽  
Uniqueness Of The Solution ◽  
Independent Brownian Motion ◽  
Teugels Martingales

We study the solution of one-dimensional generalized backward stochastic differential equation driven by Teugels martingales and an independent Brownian motion. We prove existence and uniqueness of the solution when the coefficient verifies some conditions of Lipschitz. If the coefficient is left continuous, increasing, and bounded, we prove the existence of a solution.

Fractional anticipated BSDEs with stochastic Lipschitz coefficients

2018 ◽  
Vol 26 (3) ◽  
pp. 143-161
Author(s):  
Ahmadou Bamba Sow ◽  
Bassirou Kor Diouf
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Fractional Brownian Motion ◽  
Comparison Theorem ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equation ◽  
Hurst Parameter ◽  
Uniqueness Of A Solution

Abstract In this paper, we deal with an anticipated backward stochastic differential equation driven by a fractional Brownian motion with Hurst parameter {H\in(1/2,1)} . We essentially establish existence and uniqueness of a solution in the case of stochastic Lipschitz coefficients and prove a comparison theorem in a specific case.

Stochastic variational inequality and reflected BSDEs with jumps and RCLL obstacle

2017 ◽  
Vol 0 (0) ◽  
Author(s):  
Abou Sene ◽  
Aboubakary Diakhaby
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Variational Inequality ◽  
Stochastic Differential Equation ◽  
Point Process ◽  
Poisson Point Process ◽  
Backward Stochastic Differential Equation ◽  
One Dimensional ◽  
Stochastic Variational Inequality ◽  
Reflected Bsdes

AbstractIn this paper, we consider a class of one-dimensional reflected Backward Stochastic Differential Equation (BSDE for short) when the noise is driven by a Brownian motion and an independent Poisson point process. Using a stochastic variational inequality, we characterize its solution.

scholarly journals Mean-field anticipated BSDEs driven by time-changed Lévy noises

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Youxin Liu ◽  
Yang Dai
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equation ◽  
Mean Field ◽  
Iterative Sequence ◽  
Uniqueness Of The Solution ◽  
The Fixed Point Theorem

Abstract The objective of this work is to show a new kind of mean-field anticipated backward stochastic differential equation (in short MF-ABSDE) driven by time-changed Lévy noises. We give two methods to prove the existence and uniqueness of the solution of those equations by the fixed point theorem and the Picard iterative sequence. Finally, we obtain a comparison theorem for the solutions.

scholarly journals Lp (p ≥ 1) solutions of multidimensional BSDEs with monotone generators in general time intervals

2014 ◽  
Vol 15 (01) ◽  
pp. 1550002 ◽  
Author(s):  
Li-Shun Xiao ◽  
Sheng-Jun Fan ◽  
Na Xu
Keyword(s):  
Differential Equation ◽  
Weak Convergence ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Additional Assumption ◽  
Backward Stochastic Differential Equation ◽  
Time Interval ◽  
Time Intervals ◽  
Lipschitz Continuous ◽  
General Time

In this paper, we are interested in solving general time interval multidimensional backward stochastic differential equation in Lp (p ≥ 1). We first study the existence and uniqueness for Lp (p > 1) solutions by the method of convolution and weak convergence when the generator is monotonic in y and Lipschitz continuous in z both non-uniformly with respect to t. Then we obtain the existence and uniqueness for L1 solutions with an additional assumption that the generator has a sublinear growth in z non-uniformly with respect to t.

Smooth first-passage densities for one-dimensional diffusions

1987 ◽  
Vol 24 (02) ◽  
pp. 370-377 ◽  
Author(s):  
E. J. Pauwels
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Time Scale ◽  
First Passage ◽  
One Dimensional ◽  
Drift Coefficient

The purpose of this paper is to show that smoothness conditions on the diffusion and drift coefficient of a one-dimensional stochastic differential equation imply the existence and smoothness of a first-passage density. In order to be able to prove this, we shall show that Brownian motion conditioned to first hit a point at a specified time has the same distribution as a Bessel (3)-process with changed time scale.

BSDE with rcll reflecting barrier driven by a Lévy process

2020 ◽  
Vol 28 (1) ◽  
pp. 63-77 ◽  
Author(s):  
Mohamed El Jamali ◽  
Mohamed El Otmani
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Lévy Process ◽  
Backward Stochastic Differential Equation ◽  
American Option ◽  
Levy Process ◽  
Fair Price ◽  
Penalization Method ◽  
Uniqueness Of A Solution

AbstractIn this paper, we study the solution of a backward stochastic differential equation driven by a Lévy process with one rcll reflecting barrier. We show the existence and uniqueness of a solution by means of the penalization method when the coefficient is stochastic Lipschitz. As an application, we give a fair price of an American option.

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