In this paper, we study the problem of solving Seal’s type partial integro-differential
equations (PIDEs) for the classical compound Poisson risk model. A data-driven deep neural network
(DNN) method is proposed to calculate finite-time survival probability, and an alternative scheme
is also investigated when claim payments are exponentially distributed. The DNN method is then
extended to the numerical solution of generalized PIDEs. Numerical approximation results under
different claim distributions are given, which show that the proposed scheme can obtain accurate
results under different claim distributions.
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