Delft University of Technology Researchers Have Provided New Data on Risk Management (The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations): Insurance – Risk Management

2022 APR 07 (NewsRx) -- By a News Reporter-Staff News Editor at Insurance Daily News -- Current study results on risk management have been published. According to news reporting from Delft, Netherlands, by NewsRx journalists, research stated, “We propose an accurate data-driven numerical scheme to solve stochastic differential equations (SDEs), by taking large time steps.”

Our news correspondents obtained a quote from the research from Delft University of Technology: “The SDE discretization is built up by means of the polynomial chaos expansion method, on the basis of accurately determined stochastic collocation (SC) points. By employing an artificial neural network to learn these SC points, we can perform Monte Carlo simulations with large time steps. Basic error analysis indicates that this data-driven scheme results in accurate SDE solutions in the sense of strong convergence, provided the learning methodology is robust and accurate. With a method variant called the compression-decompression collocation and interpolation technique, we can drastically reduce the number of neural network functions that have to be learned, so that computational speed is enhanced. As a proof of concept, 1D numerical experiments confirm a high-quality strong convergence error when using large time steps, and the novel scheme outperforms some classical numerical SDE discretizations.”

According to the news reporters, the research concluded: “Some applications, here in financial option valuation, are also presented.”

For more information on this research see: The Seven-League Scheme: Deep Learning for Large Time Step Monte Carlo Simulations of Stochastic Differential Equations. Risks, 2022,10(47):47. (Risks - http://www.mdpi.com/journal/risks). The publisher for Risks is MDPI AG.

A free version of this journal article is available at https://doi.org/10.3390/risks10030047.

Our news editors report that more information may be obtained by contacting Shuaiqiang Liu, Applied Mathematics (DIAM), Delft University of Technology, 2628 CD Delft, Netherlands. Additional authors for this research include Lech A. Grzelak, Cornelis W. Oosterlee.

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