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Iterative improvement of lower and upper bounds for backward SDEs

Bender,Christian
; 
Gärtner,Christian
; 
Schweizer,Nikolaus
Abstract
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semilinear partial differential equations. Solving such dynamic programs numerically requires the approximation of nested conditional expectations, i.e., iterated integrals of previous approximations. Our approach allows us to compute and iteratively improve upper and lower bounds on the true solution, starting from an arbitrary and possibly crude input approximation. We demonstrate the benefits of our approach in a high-dimensional financial application.
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Date
2017-01-01
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Tilburg University Research Output Collection
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Keywords
backward stochastic differential equations, dynamic programming, iterated improvement, Monte Carlo
Citation
Bender, C, Gärtner, C & Schweizer, N 2017, 'Iterative improvement of lower and upper bounds for backward SDEs', SIAM Journal on Scientific Computing, vol. 39, no. 2, pp. B442-B466. https://doi.org/10.1137/16M1081348
URI
https://hdl.handle.net/20.500.14602/66732
License
info:eu-repo/semantics/closedAccess
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