标题： 量化小型固定福利养老金计划的死亡风险 显示英文标题

标题： Quantifying mortality risk in small defined-benefit pension schemes

摘要： 小型固定收益养老金计划面临的风险之一是成员数量不足，无法消除特定的死亡率风险，即成员数量不足以有效分散死亡率风险。 这意味着，当计划中的成员数量较少时，与大型计划相比，负债价值显著偏离预期负债价值的风险会增加。 我们通过考察计划负债价值相对于其期望值的变化系数来量化这一风险。 我们研究了变化系数如何随成员数量的变化而变化，并发现即使计划中有几百名成员，特定死亡率风险仍可能显著。 使用随机死亡率模型可以降低特定死亡率风险，但代价是增加了计划的整体死亡率风险。 接下来，我们量化了计划执行部分的死亡率风险集中程度，其中执行人员获得的福利高于非执行人员的福利。 我们使用欧拉资本分配原则在执行和非执行部分之间分配负债价值的总标准差。 我们发现，根据成员福利金额进行分配时，分配到执行部分的标准差比例比建议的比例更高。 尽管结果对选择的死亡率模型敏感，但它们确实表明，应在一个计划的部分内部监控和管理计划的死亡率风险，而不仅仅是从整个计划的角度进行管理。 显示英文摘要

摘要： A risk of small defined-benefit pension schemes is that there are too few members to eliminate idiosyncratic mortality risk, that is there are too few members to effectively pool mortality risk. This means that when there are few members in the scheme, there is an increased risk of the liability value deviating significantly from the expected liability value, as compared to a large scheme. We quantify this risk through examining the coefficient of variation of a scheme's liability value relative to its expected value. We examine how the coefficient of variation varies with the number of members and find that, even with a few hundred members in the scheme, idiosyncratic mortality risk may still be significant. Using a stochastic mortality model reduces the idiosyncratic mortality risk but at the cost of increasing the overall mortality risk in the scheme. Next we quantify the amount of the mortality risk concentrated in the executive section of the scheme, where the executives receive a benefit that is higher than the non-executive benefit. We use the Euler capital allocation principle to allocate the total standard deviation of the liability value between the executive and non-executive sections. We find that the proportion of the standard deviation allocated to the executive section is higher than is suggested by an allocation based on the members' benefit amounts. While the results are sensitive to the choice of mortality model, they do suggest that the mortality risk of the scheme should be monitored and managed within the sections of a scheme, and not only on a scheme-wide basis.