For a large motor insurance portfolio, on an open environment, we study the impact of experience rating in finite and continuous time ruin probabilities. We consider a model for calculating ruin probabilities applicable to large portfolios with a Markovian Bonus‐Malus System (BMS), based on claim counts, for an automobile portfolio using the classical risk framework model. New challenges are brought when an open portfolio scenario is introduced. When compared with a classical BMS approach ruin probabilities may change significantly. By using a BMS of a Portuguese insurer, we illustrate and discuss the impact of the proposed formulation on the initial surplus required to target a given ruin probability. Under an open portfolio setup, we show that we may have a significant impact on capital requirements when compared with the classical BMS, by having a significant reduction on the initial surplus needed to maintain a fixed level of the ruin probability.

中文翻译：

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具有基于索赔计数的奖金-Malus 系统的开放式汽车投资组合的毁坏概率和资本要求

对于大型汽车保险组合，在开放环境中，我们研究了经验评级对有限和连续时间破产概率的影响。我们考虑了一个模型，用于计算适用于大型投资组合的破产概率，该模型基于索赔计数，适用于使用经典风险框架模型的汽车投资组合。引入开放式投资组合方案时会带来新的挑战。与经典的 BMS 方法相比，破产概率可能会发生显着变化。通过使用葡萄牙保险公司的 BMS，我们说明并讨论了拟议公式对针对给定破产概率所需的初始盈余的影响。在开放的投资组合设置下，我们表明与经典 BMS 相比，我们可能对资本要求产生重大影响，