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This paper considers the optimal dividend and capital injection
strategies in the classical risk model with randomized observation periods. Assume that ruin
is prohibited. We aim to maximise the expected discounted dividend payments minus the expected
penalised discounted capital injections. We derive the associated Hamilton-Jacobi-Bellman
(HJB) equation and prove the verification theorem. The optimal control strategy and the
optimal value function are obtained under the assumption that the claim sizes are
exponentially distributed.