Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/258089 
Year of Publication: 
2020
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 8 [Issue:] 4 [Article No.:] 136 [Publisher:] MDPI [Place:] Basel [Year:] 2020 [Pages:] 1-18
Publisher: 
MDPI, Basel
Abstract: 
In insurance mathematics, optimal control problems over an infinite time horizon arise when computing risk measures. 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. 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.
Subjects: 
backward stochastic differential equations
semilinear elliptic partial differential
equations
stochastic optimal control
unbounded random terminal time
machine learning
deep neural networks
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Creative Commons License: 
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Document Type: 
Article
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