This paper extends the known result due to Belhaj[1] who found the optimal dividend policy is of a barrier type for a jump-diffusion model with exponentially distributed jumps. It turns out that there can be essentially two different solutions depending on the model's parameters. It also deals with the optimal control problem for the jump-diffusion process with solvency constraints. The objective of the corporation is to maximize the cumulative expected discounted dividends payout with solvency constraints. It is well known that under some reasonable assumptions, optimal dividend strategy is a barrier strategy, i.e., there is a level b* so that whenever surplus goes above b*, the excess is paid out as dividends. However, the optimal level b* may be unacceptably low from a solvency point of view. Therefore, some constraints should imposed on an insurance company such as to pay out dividends unless the surplus has reached a level b0 > b*. We show that in this case a barrier strategy at b0 is optimal
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机译：本文扩展了已知的结果，这是由于Belhaj [1]发现最优指数分配策略是具有指数分布跳跃的跳跃扩散模型的障碍类型。事实证明，根据模型的参数，实际上可以有两种不同的解决方案。它还解决了具有偿付能力约束的跳跃扩散过程的最优控制问题。公司的目标是在有偿付能力约束的情况下最大化累积的预期折现股息支出。众所周知，在某些合理的假设下，最优股利策略是一个障碍策略，即有一个水平b *，以便每当盈余超过b *时，盈余就被作为股息支付。然而，从偿付能力的观点来看，最佳水平b *可能低得令人无法接受。因此，除非盈余达到b0> b *的水平，否则应该对保险公司施加一些约束，例如派发股息。我们表明，在这种情况下，b0处的障碍策略是最佳的
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