Sobolev solution for semilinear PDE with obstacle under monotonicity condition.
Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations
In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.
The smallest g-supermartingale and reflected BSDE with single and double obstacles
Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations
In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.
Reflected backward stochastic differential equations with two RCLL barriers
In this paper we consider BSDEs with Lipschitz coefficient reflected on two discontinuous (RCLL) barriers. In this case, we prove first the existence and uniqueness of the solution, then we also prove the convergence of the solutions of the penalized equations to the solution of the RBSDE. Since the method used in the case of continuous barriers (see Cvitanic and Karatzas, (1996) 2024–2056 and Lepeltier and San Martín, (2004) 162–175) does not work, we develop...
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