标题： de Finetti的分红问题与二维保险风险过程的脉冲控制 显示英文标题

标题： De Finetti's dividend problem and impulse control for a two-dimensional insurance risk process

摘要： 考虑两家保险公司（或者同一家公司的两个分支），它们以不同的速率收取保费，并且在支付每笔索赔时按照固定比例分摊费用（为简单起见，我们假设这些比例相等）。 我们根据泊松过程来建模索赔的发生。 当相应的二维风险过程首次离开正象限时，破产就发生了。 我们将考虑受控过程的两种情形：反射和脉冲控制。 在第一种情况下，当二维风险过程退出固定区域时支付股息。 在第二种情形下，每当过程到达水平线时，通过支付股息将其降低到正象限中的某个固定点，然后等待下一次索赔的到来。 在这两种模型中，我们都计算直到破产为止的贴现累积股息支付。 本文是理解两个投资组合之间的依赖性对联合最优股息支付策略影响的首次尝试。 例如，在比例再保险的情况下，可以观察到一个有趣的现象，即最优屏障的选择取决于初始储备金。 这与一维 Cramér-Lundberg 模型形成对比，在该模型中，屏障的最佳选择对所有初始储备金都是相同的。 显示英文摘要

摘要： Consider two insurance companies (or two branches of the same company) that receive premiums at different rates and then split the amount they pay in fixed proportions for each claim (for simplicity we assume that they are equal). We model the occurrence of claims according to a Poisson process. The ruin is achieved when the corresponding two-dimensional risk process first leaves the positive quadrant. We will consider two scenarios of the controlled process: refraction and impulse control. In the first case the dividends are payed out when the two-dimensional risk process exits the fixed region. In the second scenario, whenever the process hits the horizontal line, it is reduced by paying dividends to some fixed point in the positive quadrant where it waits for the next claim to arrive. In both models we calculate the discounted cumulative dividend payments until the ruin. This paper is the first attempt to understand the effect of dependencies of two portfolios on the joint optimal strategy of paying dividends. For example in case of proportional reinsurance one can observe the interesting phenomenon that choice of the optimal barrier depends on the initial reserves. This is in contrast with the one-dimensional Cram\'{e}r-Lundberg model where the optimal choice of the barrier is uniform for all initial reserves.