Wang Cuilian, Liu Xiao, Xu Lin. The Optimal Dividend and Capital Injection Strategies in the Classical Risk Model with Randomized Observation Periods[J]. Chinese Journal of Applied Probability and Statistics, 2014, 30(6): 661-672.
Citation: Wang Cuilian, Liu Xiao, Xu Lin. The Optimal Dividend and Capital Injection Strategies in the Classical Risk Model with Randomized Observation Periods[J]. Chinese Journal of Applied Probability and Statistics, 2014, 30(6): 661-672.

The Optimal Dividend and Capital Injection Strategies in the Classical Risk Model with Randomized Observation Periods

  • 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.
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