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In insurance mathematics optimal control problems over an infinite timehorizon arise when computing risk measures. Their solutions correspond tosolutions of deterministic semilinear (degenerate) elliptic partialdifferential equations. In this paper we propose a deep neural networkalgorithm for solving such partial differential equations in high dimensions.The algorithm is based on the correspondence of elliptic partial differentialequations to backward stochastic differential equations with random terminaltime.

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