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 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.

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.

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.

scholarly journals Backward SDEs and infinite horizon stochastic optimal control

2019 ◽  
Vol 25 ◽  
pp. 31 ◽  
Author(s):  
Fulvia Confortola ◽  
Andrea Cosso ◽  
Marco Fuhrman
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Brownian Motion ◽  
Optimal Control Problem ◽  
Stochastic Differential Equation ◽  
Control Problem ◽  
Backward Stochastic Differential Equation ◽  
Infinite Horizon ◽  
Jump Process ◽  
Elliptic Type

We study an optimal control problem on infinite horizon for a controlled stochastic differential equation driven by Brownian motion, with a discounted reward functional. The equation may have memory or delay effects in the coefficients, both with respect to state and control, and the noise can be degenerate. We prove that the value, i.e. the supremum of the reward functional over all admissible controls, can be represented by the solution of an associated backward stochastic differential equation (BSDE) driven by the Brownian motion and an auxiliary independent Poisson process and having a sign constraint on jumps. In the Markovian case when the coefficients depend only on the present values of the state and the control, we prove that the BSDE can be used to construct the solution, in the sense of viscosity theory, to the corresponding Hamilton-Jacobi-Bellman partial differential equation of elliptic type on the whole space, so that it provides us with a Feynman-Kac representation in this fully nonlinear context. The method of proof consists in showing that the value of the original problem is the same as the value of an auxiliary optimal control problem (called randomized), where the control process is replaced by a fixed pure jump process and maximization is taken over a class of absolutely continuous changes of measures which affect the stochastic intensity of the jump process but leave the law of the driving Brownian motion unchanged.

Smooth first-passage densities for one-dimensional diffusions

1987 ◽  
Vol 24 (2) ◽  
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.

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