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A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics

Kremsner, Stefan; Steinicke, Alexander; Szölgyenyi, … - In: Risks : open access journal 8 (2020) 4/136, pp. 1-18

In insurance mathematics, optimal control problems over an infinite time horizon arise when computing risk measures. An …

Persistent link: https://www.econbiz.de/10012391761

Asymptotic expansion and deep neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with nonlinear coefficients

Takahashi, Akihiko; Yamada, Toshihiro - 2021

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Numerical Methods in Computational Finance : A Partial Differential Equation (PDE/FDM) Approach

Duffy, Daniel J. - 2022

for One‐Factor Problems -- CHAPTER 1 Real Analysis Foundations for this Book -- 1.1 Introduction and Objectives -- 1 …

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Approximation of expectation of diffusion processes based on Lie algebra and Malliavin calculus

Kusuoka, Shigeo - In: Advances in mathematical economics 6 (2004), pp. 69-83

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Functional Itô Calculus

Dupire, Bruno - 2009

Itô calculus deals with functions of the current state whilst we deal with functions of the current path to acknowledge the fact that often the impact of randomness is cumulative. We express the differential of the functional in terms of adequately defined partial derivatives to obtain an Itô...

Persistent link: https://www.econbiz.de/10013157930