Key result
Oblique projection scheme achieves error order of 1/2 - epsilon for multidimensional backward stochastic equations.
Why the study?
Discrete-time approximation methods for multidimensional reflected BSDEs require improved schemes and error control beyond existing penalizing approaches.
Key points are not available for this paper at this time.
Comparison
Oblique projection scheme vs penalizing approaches
Design
Mathematical study of discrete-time approximation algorithms for multidimensional reflected BSDEs
New discretization scheme for reflected BSDEs may aid stochastic modeling; leaves open validation and clinical translation in cardiovascular applications.
In this paper, we study the discrete-time approximation of multidimensional reflected BSDEs of the type of those presented by Hu and Tang [Probab. Theory Related Fields 147 (2010) 89–121] and generalized by Hamadène and Zhang [Stochastic Process. Appl. 120 (2010) 403–426]. In comparison to the penalizing approach followed by Hamadène and Jeanblanc [Math. Oper. Res. 32 (2007) 182–192] or Elie and Kharroubi [Statist. Probab. Lett. 80 (2010) 1388–1396], we study a more natural scheme based on oblique projections. We provide a control on the error of the algorithm by introducing and studying the notion of multidimensional discretely reflected BSDE. In the particular case where the driver does not depend on the variable Z, the error on the grid points is of order ½ − ε, ε > 0.
No takes yet. Share an insight, caveat, or question.
Chassagneux et al. (2012) studied this question. The authors present a discrete-time approximation scheme based on oblique projections for multidimensional reflected backward stochastic differential equations, achieving an error order of 1/2 - epsilon.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: