A PRIMAL–DUAL ALGORITHM FOR BSDES
By Christian Bender, Nikolaus Schweizer, J. Zhuo. 2013
52 citations recorded by the source corpus.
We generalize the primal–dual methodology, which is popular in the pricing of early‐exercise options, to a backward dynamic programming equation associated with time discretization schemes of (reflected) backward stochastic differential equations (BSDEs). Taking as an input some approximate solution of the backward dynamic program, which was precomputed, e.g., by least‐squares Monte Carlo, this methodology enables us to construct a confidence interval for the unknown true solution of the time‐discretized (reflected) BSDE at time 0. We numerically demonstrate the practical applicability of our method in two 5‐dimensional nonlinear pricing problems where tight price bounds were previously unavailable.
Subfields: Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/495fbfafd0de0053a61ee36dbfcc514c72fedaeb
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In Finance
- Arnulf Jentzen
- Christian Beck
- Jiequn Han
- W. E
- Martin Hutzenthaler
- Philippe von Wurstemberger
- Xuerong Mao
- Sotirios Sabanis
In Management Science and Operations Research
- Christian Beck
- W. E
- Martin Hutzenthaler
- Arnulf Jentzen
- Philippe von Wurstemberger
- Jiequn Han
- Sotirios Sabanis
- Xuerong Mao
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”
- 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”
- Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations (2017, methodology): “, [2,3,5,8,13,14] where this example has been used as a test example for numerical methods for BSDEs).”
- Solving high-dimensional partial differential equations using deep learning (2017, methodology): “To demonstrate the effectiveness of the deep BSDE method, we study a special case of the recursive valuation model with default risk [16, 17].”