arXiv:2412.03405v3 Announce Type: replace-cross Abstract: Motivated by dynamic risk measures and conditional $g$-expectations, in this work we propose a numerical method to approximate the solution operator given by a Backward Stochastic Differential Equation (BSDE). The main ingredients for this are the Wiener chaos decomposition and the classical Euler scheme for BSDEs. We show convergence of this scheme under very mild assumptions, and provide a rate of convergence in more restrictive cases. We then implement it using neural networks, and we present several numerical examples where we can c
The increasing complexity of financial models and the computational demands of dynamic risk measures are driving innovation in numerical methods for solving BSDEs.
This development can lead to more accurate and efficient risk management and financial modeling, critical for stability in complex economic systems.
The ability to approximate solution operators for BSDEs using neural networks provides a more robust and scalable approach to financial and control problems.
- · Financial institutions
- · Quantitative analysts
- · AI/Machine Learning in finance
- · Traditional numerical methods (in some applications)
- · Institutions without advanced computational capabilities
Improved accuracy and speed in pricing complex derivatives and managing dynamic risk.
Reduced operational costs and increased sophistication in financial product development and regulatory compliance.
The development of new financial products and services previously intractable due to computational limits, potentially altering market structures.
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Read at arXiv cs.LG