Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics
Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematics
In recent years a large literature on deep learning based methods for the numerical solution partial differential equations has emerged; results for integro-differential equations on the other hand are scarce. In this paper we study deep neural network algorithms for solving linear and semilinear parabolic partial integro-differential equations with boundary conditions in high dimension. To show the viability of our approach we discuss several case studies from insurance and finance.
24 pages
502009 Corporate finance, FOS: Computer and information sciences, 101024 Wahrscheinlichkeitstheorie, Probability (math.PR), Computational Finance (q-fin.CP), Machine Learning (stat.ML), Numerical Analysis (math.NA), 101007 Financial mathematics, FOS: Economics and business, 502009 Finanzwirtschaft, Quantitative Finance - Computational Finance, Statistics - Machine Learning, 101007 Finanzmathematik, FOS: Mathematics, 101024 Probability theory, Mathematics - Numerical Analysis, Mathematics - Probability
502009 Corporate finance, FOS: Computer and information sciences, 101024 Wahrscheinlichkeitstheorie, Probability (math.PR), Computational Finance (q-fin.CP), Machine Learning (stat.ML), Numerical Analysis (math.NA), 101007 Financial mathematics, FOS: Economics and business, 502009 Finanzwirtschaft, Quantitative Finance - Computational Finance, Statistics - Machine Learning, 101007 Finanzmathematik, FOS: Mathematics, 101024 Probability theory, Mathematics - Numerical Analysis, Mathematics - Probability
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