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.

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.

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 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 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.

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.

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 Multi-valued backward stochastic differential equations with regime switching

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ruijuan Deng ◽  
Yong Ren
Keyword(s):  
Markov Chain ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Regime Switching ◽  
Original System ◽  
Backward Stochastic Differential Equations ◽  
Lower Semi ◽  
Finite State ◽  
Uniqueness Of The Solution ◽  
Continuous Convex Function

AbstractThe paper considers a class of multi-valued backward stochastic differential equations with subdifferential of a lower semi-continuous convex function with regime switching, whose generator is a continuous-time Markov chain with a finite state space. Firstly, we get the existence and uniqueness of the solution by the penalization method. Secondly, we prove that the solution of the original system is weakly convergent. Finally, we give an application to the homogenization of a class of multi-valued PDEs with Markov chain.

scholarly journals Anticipated backward SDEs with jumps and quadratic-exponential growth drivers

2019 ◽  
Vol 19 (03) ◽  
pp. 1950020
Author(s):  
Masaaki Fujii ◽  
Akihiko Takahashi
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Unique Solution ◽  
Exponential Growth ◽  
Linear Growth ◽  
Uniform Norm ◽  
Backward Stochastic Differential Equations ◽  
Forward Process ◽  
Backward Sdes

In this paper, we study a class of Anticipated Backward Stochastic Differential Equations (ABSDE) with jumps. The solution of the ABSDE is a triple [Formula: see text] where [Formula: see text] is a semimartingale, and [Formula: see text] are the diffusion and jump coefficients. We allow the driver of the ABSDE to have linear growth on the uniform norm of [Formula: see text]’s future paths, as well as quadratic and exponential growth on the spot values of [Formula: see text], respectively. The existence of the unique solution is proved for Markovian and non-Markovian settings with different structural assumptions on the driver. In the former case, some regularities on [Formula: see text] with respect to the forward process are also obtained.

scholarly journals Existence and Uniqueness Theorem for Stochastic Differential Equations with Self-Exciting Switching

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Guixin Hu ◽  
Ke Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Sufficient Condition ◽  
Existence And Uniqueness Theorem ◽  
Uniqueness Of The Solution

We introduce a new kind of equation, stochastic differential equations with self-exciting switching. Firstly, we give some preliminaries for this kind of equation, and then, we get the main results of our paper; that is, we gave the sufficient condition which can guarantee the existence and uniqueness of the solution.

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