In this paper, we consider the optimal dividend problem in the spectrally positive L\'{e}vy model with regime switching. By an auxiliary optimal problem, the principle of dynamic programming and the fluctuation theory of L\'{e}vy processes, we show that optimal strategy is a modulated barrier strategy. The value function and the optimal dividend barrier are obtained by iteration.
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YE Chuanxiu; ZHAO Yongxia. Optimal Dividend Strategy in the Spectrally PostiveL\'{e}vy Risk Model with Regime Switching. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2020, 36(1): 71-85.