Solving high dimensional FBSDE with deep signature techniques with application to nonlinear options pricing
arxiv(2024)
摘要
We report two methods for solving FBSDEs of path dependent types of high
dimensions. Specifically, we propose a deep learning framework for solving such
problems using path signatures as underlying features. Our two methods
(forward/backward) demonstrate comparable/better accuracy and efficiency
compared to the state of the art techniques. More importantly, we are able to
solve the problem of high dimension which is a limitation in the conventional
methods. We also provide convergence proof for both methods with the proof of
the backward methods in the Markovian case.
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