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.

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.

Deplay BSDEs driven by fractional Brownian motion

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Sadibou Aidara ◽  
Ibrahima Sane
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Existence And Uniqueness ◽  
Stochastic Integral ◽  
Hurst Parameter ◽  
The Past ◽  
Type Integral ◽  
Divergence Type ◽  
Uniqueness Of A Solution

Abstract This paper deals with a class of deplay backward stochastic differential equations driven by fractional Brownian motion (with Hurst parameter H greater than 1 2 {\frac{1}{2}} ). In this type of equation, a generator at time t can depend not only on the present but also the past solutions. We essentially establish existence and uniqueness of a solution in the case of Lipschitz coefficients and non-Lipschitz coefficients. The stochastic integral used throughout this paper is the divergence-type integral.

scholarly journals Lp-SOLUTIONS FOR REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS

2012 ◽  
Vol 12 (02) ◽  
pp. 1150016 ◽  
Author(s):  
SAÏD HAMADÈNE ◽  
ALEXANDRE POPIER
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equation ◽  
Snell Envelope ◽  
Equation Problem ◽  
Class Of Functions ◽  
Uniqueness Of A Solution ◽  
Lp Solutions

This paper deals with the problem of existence and uniqueness of a solution for a backward stochastic differential equation (BSDE for short) with one reflecting barrier in the case when the terminal value, the generator and the obstacle process are Lp-integrable with p ∈ ]1, 2[. To construct the solution we use two methods: penalization and Snell envelope. As an application we broaden the class of functions for which the related obstacle partial differential equation problem has a unique viscosity solution.

scholarly journals A Study on a New Class of Backward Stochastic Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Ping He ◽  
Yong Ren ◽  
Defei Zhang
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Comparison Theorem ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equation ◽  
New Class ◽  
The Past ◽  
The Future ◽  
New Type

The existence and uniqueness for a new type of backward stochastic differential equation when the generator includes the values of solutions of the past, the present, and the future are obtained in this paper. An important comparison theorem for this sort of BSDEs is also proved.

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.

Harnack-type inequality for linear fractional stochastic equations

2020 ◽  
Vol 28 (4) ◽  
pp. 281-290
Author(s):  
Brahim Boufoussi ◽  
Soufiane Mouchtabih
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Fractional Brownian Motion ◽  
Type Inequality ◽  
Stochastic Equations ◽  
Coupling Method ◽  
Hurst Parameter ◽  
Brownian Sheet ◽  
Harnack Type Inequality

AbstractUsing the coupling method and Girsanov theorem, we prove a Harnack-type inequality for a stochastic differential equation with non-Lipschitz drift and driven by a fractional Brownian motion with Hurst parameter {H<\frac{1}{2}}. We also investigate this inequality for a stochastic differential equation driven by an additive fractional Brownian sheet.

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