scholarly journals Backward stochastic differential equations with stochastic monotone coefficients

2004 ◽  
Vol 2004 (4) ◽  
pp. 317-335 ◽  
Author(s):  
K. Bahlali ◽  
A. Elouaflin ◽  
M. N'zi
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Nonlinear Pdes ◽  
Monotonicity Condition ◽  
Stochastic Monotonicity ◽  
Monotone Coefficients ◽  
Terminal Time

We prove an existence and uniqueness result for backward stochastic differential equations whose coefficients satisfy a stochastic monotonicity condition. In this setting, we deal with both constant and random terminal times. In the random case, the terminal time is allowed to take infinite values. But in a Markovian framework, that is coupled with a forward SDE, our result provides a probabilistic interpretation of solutions to nonlinear PDEs.

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

REFLECTED BSDES WITH STOCHASTIC MONOTONE GENERATOR AND APPLICATION TO VALUING AMERICAN OPTIONS

2020 ◽  
Vol 23 (05) ◽  
pp. 2050034
Author(s):  
MOHAMED MARZOUGUE
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
American Options ◽  
Growth Conditions ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Monotonicity ◽  
Uniqueness Of The Solution ◽  
Fair Valuation ◽  
Reflected Bsdes

In this paper, we prove the existence and uniqueness of the solution to backward stochastic differential equations with lower reflecting barrier in a Brownian setting under stochastic monotonicity and general increasing growth conditions. As an application, we study the fair valuation of American options.

scholarly journals Reflected backward stochastic differential equations under monotonicity and general increasing growth conditions

2005 ◽  
Vol 37 (1) ◽  
pp. 134-159 ◽  
Author(s):  
J.-P. Lepeltier ◽  
A. Matoussi ◽  
M. Xu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Growth Conditions ◽  
Backward Stochastic Differential Equations ◽  
Contingent Claim ◽  
Terminal Time ◽  
Uniqueness Of The Solution ◽  
American Contingent Claim

We prove the existence and uniqueness of the solution to certain reflected backward stochastic differential equations (RBSDEs) with one continuous barrier and deterministic terminal time, under monotonicity, and general increasing growth conditions on the associated coefficient. As an application, we obtain, in some constraint cases, the price of an American contingent claim as the unique solution of such an RBSDE.

scholarly journals Solutions and comparison theorems for anticipated backward stochastic differential equations with non-Lipschitz generators

2016 ◽  
Vol 12 (4) ◽  
pp. 6139-6147
Author(s):  
Xuecheng XU ◽  
Min Chen
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Comparison Theorems ◽  
One Dimensional

This paper is devoted to solving multidimensional anticipated backward stochastic differential equations (anticipated BSDEs for short) with a kind of non-Lipschitz generators. We establish the existence and uniqueness result for L2 solutions of this kind of anticipated BSDEs, and establish the corresponding one-dimensional comparison theorems for the type of anticipated BSDEs. Our results improve some known results.

scholarly journals Reflected backward stochastic differential equations under monotonicity and general increasing growth conditions

2005 ◽  
Vol 37 (01) ◽  
pp. 134-159 ◽  
Author(s):  
J.-P. Lepeltier ◽  
A. Matoussi ◽  
M. Xu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Growth Conditions ◽  
Backward Stochastic Differential Equations ◽  
Contingent Claim ◽  
Terminal Time ◽  
Uniqueness Of The Solution ◽  
American Contingent Claim

We prove the existence and uniqueness of the solution to certain reflected backward stochastic differential equations (RBSDEs) with one continuous barrier and deterministic terminal time, under monotonicity, and general increasing growth conditions on the associated coefficient. As an application, we obtain, in some constraint cases, the price of an American contingent claim as the unique solution of such an RBSDE.

Reflected backward stochastic differential equations with time-delayed generators

2018 ◽  
Vol 26 (1) ◽  
pp. 11-22
Author(s):  
Navegué Tuo ◽  
Harouna Coulibaly ◽  
Auguste Aman
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Penalization Method ◽  
One Dimensional

AbstractThis paper is devoted to establish an existence and uniqueness result of one-dimensional reflected backward stochastic differential equations with time-delayed generators (RBSDEs with time-delayed generators, in short). Our proof is based on approximation via a penalization method.

scholarly journals Solutions to BSDEs Driven by Multidimensional Fractional Brownian Motions

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Jie Miao ◽  
Xu Yang
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Conditional Expectation ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Fixed Point Principle ◽  
Fractional Ito Formula

We study more general backward stochastic differential equations driven by multidimensional fractional Brownian motions. Introducing the concept of the multidimensional fractional (or quasi-) conditional expectation, we study some of its properties. Using the quasi-conditional expectation and multidimensional fractional Itô formula, we obtain the existence and uniqueness of the solutions to BSDEs driven by multidimensional fractional Brownian motions, where a fixed point principle is employed. Finally, solutions to linear fractional backward stochastic differential equations are investigated.

scholarly journals Lp Solutions of BSDEs with Stochastic Lipschitz Condition

2007 ◽  
Vol 2007 ◽  
pp. 1-14 ◽  
Author(s):  
Jiajie Wang ◽  
Qikang Ran ◽  
Qihong Chen
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lipschitz Condition ◽  
Existence And Uniqueness ◽  
Special Class ◽  
Lipschitz Continuity ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Of The Solution ◽  
Lp Solutions

We are concerned with the solutions of a special class of backward stochastic differential equations which are driven by a Brownian motion, where the uniform Lipschitz continuity is replaced by a stochastic one. We prove the existence and uniqueness of the solution in Lp with p>1.

scholarly journals Periodic Solutions for Stochastic Differential Equations Driven by General Counting Processes: Application to Malaria

2021 ◽  
Vol 13 (4) ◽  
pp. 1
Author(s):  
KOUAME Yao Simplice ◽  
NZI Modeste
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Markov Processes ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Uniqueness Result ◽  
Poisson Processes ◽  
Counting Processes ◽  
Periodic Environment

In this paper, a class of periodic stochastic differential equations driven by general counting processes (SDEsGp) is studied. First, an existence-uniqueness result for the solution of general SDEsGp based on Poisson processes with т-periodic stochastic intensity of time t has been given, for some  т> 0. Then, using the properties of periodic Markov processes, sufficient conditions for the existence and uniqueness of a periodic solution of the considered equations are obtained. We will then apply the obtained results to the propagation of malaria in a periodic environment.

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