Research from University of Graz Provides New Data on Risk Management (A Deep Neural Network Algorithm for Semilinear Elliptic PDEs with Applications in Insurance Mathematics)

2020 DEC 28 (NewsRx) -- By a News Reporter-Staff News Editor at Insurance Daily News -- New study results on insurance have been published. According to news originating from Graz, Austria, by NewsRx correspondents, research stated, “In insurance mathematics, optimal control problems over an infinite time horizon arise when computing risk measures.”

Financial supporters for this research include Austrian Science Fund.

Our news correspondents obtained a quote from the research from University of Graz: “An example of such a risk measure is the expected discounted future dividend payments. In models which take multiple economic factors into account, this problem is high-dimensional. The solutions to such control problems correspond to solutions of deterministic semilinear (degenerate) elliptic partial differential equations. In the present paper we propose a novel deep neural network algorithm for solving such partial differential equations in high dimensions in order to be able to compute the proposed risk measure in a complex high-dimensional economic environment. The method is based on the correspondence of elliptic partial differential equations to backward stochastic differential equations with unbounded random terminal time.”

According to the news reporters, the research concluded: “In particular, backward stochastic differential equations-which can be identified with solutions of elliptic partial differential equations-are approximated by means of deep neural networks.”

For more information on this research see: A Deep Neural Network Algorithm for Semilinear Elliptic PDEs with Applications in Insurance Mathematics. Risks, 2020,8(136):136. (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/risks8040136.

Our news editors report that more information may be obtained by contacting Stefan Kremsner, Department of Mathematics, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria. Additional authors for this research include Alexander Steinicke, Michaela Szolgyenyi.

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