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Stochastics, ISSN 1744-2508, 04/2020, Volume 92, Issue 3, pp. 418 - 453
We investigate conditions for solvability and Malliavin differentiability of backward stochastic differential equations driven by a Lévy process. In... 
Malliavin differentiability of BSDEs | BSDEs with jumps | quadratic BSDEs | existence and uniqueness of solutions to BSDEs | locally Lipschitz generator
Journal Article
ELECTRONIC JOURNAL OF PROBABILITY, ISSN 1083-6489, 2018, Volume 23
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 04/2019, Volume 129, Issue 4, pp. 1259 - 1286
We prove the existence of weak solution for a system of quasi-variational inequalities related to a switching problem with dynamic driven by operator... 
Switching problem | Reflected BSDEs | Semi-Dirichlet forms | Penalization scheme | Quasi-variational inequalities | EQUATIONS | BSDES | STATISTICS & PROBABILITY | OBSTACLES
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 05/2019, Volume 129, Issue 5, pp. 1492 - 1532
This article proposes a new approximation scheme for quadratic-growth BSDEs in a Markovian setting by connecting a series of semi-analytic asymptotic... 
Quadratic-growth BSDEs | Asymptotic expansion | Discretization | SCHEME | ASYMPTOTIC-EXPANSION | ALGORITHM | DISCRETE-TIME APPROXIMATION | BSDES | RISK | STATISTICS & PROBABILITY | SIMULATION | Monte Carlo method | Differential equations
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 08/2014, Volume 124, Issue 8, pp. 2654 - 2671
We introduce a new notion of local solution of backward stochastic differential equations (BSDEs) and prove that multidimensional quadratic BSDEs are locally... 
Multidimensional BSDE | Splitting BSDEs | Quadratic generator | Local equilibrium | Relative performance | STOCHASTIC DIFFERENTIAL-EQUATIONS | QUADRATIC BSDES | UNBOUNDED TERMINAL CONDITIONS | CONVEX GENERATORS | GROWTH | STATISTICS & PROBABILITY
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 2015, Volume 53, Issue 3, pp. 1440 - 1463
This paper shows that the penalized backward stochastic differential equation (BSDE), which is often used to approximate and solve the corresponding reflected... 
Penalized BSDE | Optimal switching | Reflected BSDE | Optimal stopping | Optimal control | Regime switching | optimal stopping | penalized BSDE | MATHEMATICS, APPLIED | regime switching | REFLECTED BSDES | optimal control | reflected BSDE | optimal switching | AUTOMATION & CONTROL SYSTEMS | OBSTACLES
Journal Article
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, ISSN 0363-0129, 2019, Volume 57, Issue 2, pp. 1157 - 1188
In a framework close to the one developed by Holmstrom and Milgrom [Econometrica, 55 (1987), pp. 303-328], we study the optimal contracting scheme between a... 
MATHEMATICS, APPLIED | STOCHASTIC DIFFERENTIAL-EQUATIONS | QUADRATIC BSDES | INFORMATION | STABILITY | multidimensional quadratic BSDEs | INSURANCE | Nash equilibrium | moral hazard | competition | INCENTIVES | relative performance | principal multiagents problems | CONVEX GENERATORS | EQUILIBRIUM | AUTOMATION & CONTROL SYSTEMS | 1ST-ORDER APPROACH
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 12/2015, Volume 125, Issue 12, pp. 4489 - 4542
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 2010, Volume 120, Issue 4, pp. 403 - 426
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 02/2019, Volume 129, Issue 2, pp. 634 - 673
In ergodic stochastic problems the limit of the value function Vλ of the associated discounted cost functional with infinite time horizon is studied, when the... 
Limit value | Stochastic nonexpansivity condition | BSDE | EXISTENCE | VISCOSITY SOLUTIONS | RANDOM TERMINAL TIME | BSDES | STATISTICS & PROBABILITY | LIMIT | HOMOGENIZATION | ERGODIC CONTROL
Journal Article
The Annals of Applied Probability, ISSN 1050-5164, 10/2015, Volume 25, Issue 5, pp. 2535 - 2562
We study the weak approximation of the second-order backward SDEs (2BSDEs), when the continuous driving martingales are approximated by discrete time... 
Second-order BSDEs | Numerical scheme | Robustness of BSDE | Weak approximation | robustness of BSDE | STATISTICS & PROBABILITY | weak approximation | numerical scheme | 93E15 | 65C50 | 60F05
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2017, Volume 369, Issue 12, pp. 8607 - 8641
We study natural invariance properties of functionals defined on Levy processes and show that they can be described by a simplified structure of the... 
MATHEMATICS | REPRESENTATION | BSDES | SIMULATION | WIENER CHAOS EXPANSION | JUMPS
Journal Article
ELECTRONIC JOURNAL OF PROBABILITY, ISSN 1083-6489, 2019, Volume 24
We establish an existence and uniqueness result for a class of multidimensional quadratic backward stochastic differential equations (BSDE). This class is... 
BSDES | STATISTICS & PROBABILITY | STOCHASTIC DIFFERENTIAL-EQUATIONS | quadratic BSDES | martingales | UNIQUENESS | Probability | Mathematics
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 09/2018, Volume 128, Issue 9, pp. 3118 - 3180
In this paper we consider a mean-field backward stochastic differential equation (BSDE) driven by a Brownian motion and an independent Poisson random measure.... 
Integral-PDE of mean-field type | Itô’s formula | Value function | Mean-field BSDEs with jump | BSDEs with jump | JACOBI-BELLMAN EQUATIONS | STOCHASTIC DIFFERENTIAL-EQUATIONS | MAXIMUM PRINCIPLE | STATISTICS & PROBABILITY | Ito's formula | Differential equations
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 08/2019, Volume 372, Issue 8, pp. 5891 - 5946
In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of... 
MATHEMATICS | STOCHASTIC DIFFERENTIAL-EQUATIONS | ROBUSTNESS | SEQUENCES | APPROXIMATIONS | BS-DELTA-ES | CONVERGENCE | BSDES | DRIVEN | CLOSEDNESS
Journal Article
Stochastics and Dynamics, ISSN 0219-4937, 02/2019, Volume 19, Issue 1
In this paper, we consider two classes of backward stochastic differential equations (BSDEs). First, under a Lipschitz-type condition on the generator of the... 
existence | BSDEs | unbounded generator | uniqueness | comparison theorem | QUADRATIC BSDES | CONVEX GENERATORS | GROWTH | BSDFs | NON-LIPSCHITZ | STATISTICS & PROBABILITY | Mathematics - Probability
Journal Article
Asia-Pacific Financial Markets, ISSN 1387-2834, 9/2019, Volume 26, Issue 3, pp. 391 - 408
We demonstrate that the use of asymptotic expansion as prior knowledge in the “deep BSDE solver”, which is a deep learning method for high dimensional BSDEs... 
Borrowing rates | Finance | Economic Theory/Quantitative Economics/Mathematical Methods | BSDEs | Finance, general | Deep learning | FVA | American option | Asymptotic expansion | High dimensional BSDEs | International Economics | Macroeconomics/Monetary Economics//Financial Economics | Econometrics | Deep BSDE solver | Different lending | Americanoption
Journal Article
Stochastics An International Journal of Probability and Stochastic Processes, ISSN 1744-2508, 09/2015, Volume 87, Issue 5, pp. 871 - 884
Journal Article
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