Numerical simulation of quadratic BSDEs
By Jean-François Chassagneux, Adrien Richou. 2013
65 citations recorded by the source corpus.
This article deals with the numerical approximation of Markovian backward stochastic differential equations (BSDEs) with generators of quadratic growth with respect to $z$ and bounded terminal conditions. We first study a slight modification of the classical dynamic programming equation arising from the time-discretization of BSDEs. By using a linearization argument and BMO martingales tools, we obtain a comparison theorem, a priori estimates and stability results for the solution of this scheme. Then we provide a control on the time-discretization error of order $\frac{1}{2}-\varepsilon$ for all $\varepsilon>0$. In the last part, we give a fully implementable algorithm for quadratic BSDEs based on quantization and illustrate our convergence results with numerical examples.
Subfields: Demography, Finance
View Paper: https://www.semanticscholar.org/paper/03140fe564b9b759433dcb37e3b5fbb800337bbb
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In Demography
- Arnulf Jentzen
- Christian Beck
- W. E
- Martin Hutzenthaler
- Philippe von Wurstemberger
- Jiequn Han
- Xuerong Mao
- Sotirios Sabanis
In Finance
- Arnulf Jentzen
- Christian Beck
- Jiequn Han
- W. E
- Martin Hutzenthaler
- Philippe von Wurstemberger
- Xuerong Mao
- Sotirios Sabanis
Citations in the corpus
- Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks (2019, methodology): “, [2, 6, 7, 10, 12, 13, 17, 18, 19, 20, 25, 26, 27, 28, 38, 39, 31, 32, 40, 41, 42, 43, 44, 45, 46, 57, 69, 70, 71, 72, 73, 74, 78, 79, 82, 83, 84, 85, 89, 90, 91, 96, 102, 103, 104] for probabilistic approximation methods for PDEs using discretizations of the associated backward stochastic differen”
- Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations (2017, methodology): “Lemma 4.2 (Cf., e.g., Section 4.2 in [7] and Section 8.4 in [10]) .”
- Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations (2017, methodology): “tations based on extensions of the classical Feynman-Kac formula (cf., e.g., [34, 58, 84]). We refer, e.g., to [23, 30, 65, 69, 95, 103, 104, 106] for deterministic approximation methods for PDEs, to [3, 6, 7, 13, 18, 19, 20, 21, 25, 26, 27, 28, 31, 32, 43, 44, 45, 46, 47, 48, 56, 64, 71, 72, 73, 74”