In this paper, we study two optimisation settings for an insurance company, under the constraint that the terminal surplus at a deterministic and finite time T follows a normal distribution with a given mean and a given variance. In both cases, the surplus of the insurance company is assumed to follow a Brownian motion with drift. First, we allow the insurance company to pay dividends and seek to maximise the expected discounted dividend payments or to minimise the ruin probability under the terminal distribution constraint. Here, we find explicit expressions for the optimal strategies in both cases, when the dividend strategy is updated at discrete points in time and continuously in time. Second, we let the insurance company buy a reinsurance contract for a pool of insured or a branch of business. We set the initial capital to zero in order to verify whether the premia are sufficient to buy reinsurance and to manage the risk of incoming claims in such a way that the desired risk characteristics are achieved at some terminal time without external help (represented, for instance, by a positive initial capital). We only allow for piecewise constant reinsurance strategies producing a normally distributed terminal surplus, whose mean and variance lead to a given Value at Risk or Expected Shortfall at some confidence level α. We investigate the question which admissible reinsurance strategy produces a smaller ruin probability, if the ruin-checks are due at discrete deterministic points in time.

在本文中，我们研究了保险公司的两种优化设置，在确定性和有限时间T处的终端盈余约束下服从具有给定均值和给定方差的正态分布。在这两种情况下，假设保险公司的盈余遵循带有漂移的布朗运动。首先，我们允许保险公司支付股息，并在终端分配约束下寻求最大化预期贴现股息支付或最小化破产概率。在这里，当股利策略在离散时间点和连续时间更新时，我们找到了两种情况下最优策略的显式表达式。其次，我们让保险公司为一组被保险人或一个业务分支机构购买再保险合同。我们将初始资本设置为零，以验证保费是否足以购买再保险并管理传入索赔的风险，以便在没有外部帮助的情况下在某个终端时间实现所需的风险特征（例如， ，由正初始资本）。我们只允许分段恒定再保险策略产生正态分布的终端盈余，其均值和方差导致在某个置信水平下给定的风险价值或预期缺口α。我们研究了这样的问题：如果破产检查是在离散的确定性时间点到期的话，哪种可接受的再保险策略会产生较小的破产概率。