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| Optimal Dividend Strategy in the Spectrally PostiveL\'{e}vy Risk Model with Regime Switching |
| YE Chuanxiu; ZHAO Yongxia |
| School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, China; School of Statistics, Qufu Normal University, Qufu, 273165, China |
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Abstract 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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