The problem of designing an optimal insurance strategy in a new multistep insurance model is investigated. This model introduces stepwise probabilistic constraints (Value-at-Risk constraints) on the insurer’s capital, i.e., probabilistic constraints on the insurer’s capital increments during one step. As the objective functional the mathematical expectation of the insurer’s final capital is used. The total damage to the insurer at each step is modeled by the Gaussian distribution with parameters depending on a risk sharing function selected. In contrast to traditional dynamic optimization models for insurance strategies, the approach proposed below takes into account stepwise constraints; within this approach, the Bellman functions are constructed (and hence the optimal risk sharing is found) by simply solving a sequence of static insurance optimization problems. It is demonstrated that the optimal risk sharing is the so-called stop-loss insurance.

研究了在新的多步保险模型中设计最优保险策略的问题。该模型引入了对保险公司资本的逐步概率约束（风险价值约束），即，对保险人在一步之内的资本增量的概率约束。作为目标函数，使用了保险公司最终资本的数学期望。保险公司在每个步骤的总损失由高斯分布建模，参数取决于所选的风险分担函数。与传统的保险策略动态优化模型相比，以下提出的方法考虑了逐步约束。在这种方法中，通过简单地解决一系列静态保险优化问题，就可以构造贝尔曼函数（从而找到最佳的风险分担）。事实证明，最佳的风险分担是所谓的止损保险。