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We mainly studied the dividend payout with a two-sided jumps risk model under random observation. The two-sided jumps in the model represent random claims and random returns. First, we obtained the integral differential equation of the expected dividend under the boundary conditions. Because the equations cannot be solved directly under normal circumstances, we chose the sinc numerical method here to approximate the solution of the equations. Then the error analysis of the approximate solution was carried out to illustrate the rationality of the numerical method. Finally, some concrete numerical examples were given.