WEAK SOLUTIONS OF SEMILINEAR PDEs WITH OBSTACLE(S) IN SOBOLEV SPACES AND THEIR PROBABILISTIC INTERPRETATION VIA THE RFBSDEs AND DRFBSDEs

2008 ◽  
Vol 08 (02) ◽  
pp. 247-269 ◽  
Author(s):  
YOUSSEF OUKNINE ◽  
DJIBRIL NDIAYE
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Probabilistic Interpretation ◽  
Penalization Method ◽  
Semilinear Pdes ◽  
Uniqueness Of The Solution

We prove the existence and uniqueness of the solution of a semilinear PDEs with obstacle(s) under Lipschitz condition. We give a probabilistic interpretation of the solution in Sobolev spaces using reflected forward–backward stochastic differential equations, doubly reflected forward–backward stochastic differential equations and the penalization method.

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 REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A LÉVY PROCESS

2009 ◽  
Vol 50 (4) ◽  
pp. 486-500 ◽  
Author(s):  
YONG REN ◽  
XILIANG FAN
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lévy Process ◽  
Backward Stochastic Differential Equations ◽  
Levy Process ◽  
Penalization Method ◽  
Lower Semi ◽  
Uniqueness Of The Solution ◽  
Teugels Martingales ◽  
Continuous Convex Function

AbstractIn this paper, we deal with a class of reflected backward stochastic differential equations (RBSDEs) corresponding to the subdifferential operator of a lower semi-continuous convex function, driven by Teugels martingales associated with a Lévy process. We show the existence and uniqueness of the solution for RBSDEs by means of the penalization method. As an application, we give a probabilistic interpretation for the solutions of a class of partial differential-integral inclusions.

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 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.

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.

scholarly journals Conditions to Guarantee the Existence of the Solution to Stochastic Differential Equations of Neutral Type

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1613
Author(s):  
Mun-Jin Bae ◽  
Chan-Ho Park ◽  
Young-Ho Kim
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Exponential Estimates ◽  
Analysis Theory ◽  
Linear Growth Condition ◽  
Uniqueness Of The Solution ◽  
The Uniqueness Theorem

The main purpose of this study was to demonstrate the existence and the uniqueness theorem of the solution of the neutral stochastic differential equations under sufficient conditions. As an alternative to the stochastic analysis theory of the neutral stochastic differential equations, we impose a weakened Ho¨lder condition and a weakened linear growth condition. Stochastic results are obtained for the theory of the existence and uniqueness of the solution. We first show that the conditions guarantee the existence and uniqueness; then, we show some exponential estimates for the solutions.

scholarly journals On the continuity of weak solutions of backward stochastic differential equations

10.4213/tvp15 ◽  
2007 ◽  
Vol 52 (1) ◽  
pp. 190-199 ◽  
Author(s):  
Rainer Buckdahn ◽  
Rainer Buckdahn ◽  
Ганс-Юрген Энгельберт ◽  
Hans-Jurgen Engelbert
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Weak Solutions ◽  
Backward Stochastic Differential Equations

scholarly journals Double-barriers-reflected BSDEs with jumps and viscosity solutions of parabolic integrodifferential PDEs

2005 ◽  
Vol 2005 (1) ◽  
pp. 37-53 ◽  
Author(s):  
N. Harraj ◽  
Y. Ouknine ◽  
I. Turpin
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Viscosity Solutions ◽  
Backward Stochastic Differential Equations ◽  
Probabilistic Interpretation ◽  
Reflected Bsdes

We give a probabilistic interpretation of the viscosity solutions of parabolic integrodifferential partial equations with two obstacles via the solutions of forward-backward stochastic differential equations with jumps.

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