A forward scheme for backward SDEs

We introduce a forward scheme for simulating backward SDEs. Compared to existing schemes, ours avoids high order nestings of conditional expectations backwards in time. In this way the error, when approximating the conditional expectation, depending on the time partition, is significantly reduced. B...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 117; no. 12; pp. 1793 - 1812
Main Authors Bender, Christian, Denk, Robert
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.12.2007
Elsevier Science
Elsevier
SeriesStochastic Processes and their Applications
Subjects
Applications
BSDE
BSDE Numerics Monte Carlo simulation Finance
Distribution theory
Exact sciences and technology
Finance
Insurance, economics, finance
Mathematics
Monte Carlo simulation
Numerics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Stochastic analysis
Stochastic processes
65C30
Finance
91B28
65C05
BSDE
Monte Carlo simulation
Numerics
Monte Carlo method
Partition
Error estimation
Stochastic process
Algorithm
Convergence
65C05; 65C30; 91B28
Conditional expectation
Simulation
Problem solving
BSDE; Numerics; Monte Carlo simulation; Finance
Application
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Summary:We introduce a forward scheme for simulating backward SDEs. Compared to existing schemes, ours avoids high order nestings of conditional expectations backwards in time. In this way the error, when approximating the conditional expectation, depending on the time partition, is significantly reduced. Besides this generic result, we present an implementable algorithm and prove its convergence. Finally, we demonstrate the strength of the new algorithm by solving a financial problem numerically.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2007.03.005