A stochastic approach for measuring the uncertainty of claims reserves

ABSTRACT This paper aims to obtain metrics for quantifying the variability of technical provisions for claims by making use of deterministic and stochastic models. In short, everything that the traditional methods do not provide (measures of variability and capital insufficiency) are of fundamental importance for efficient actuarial management. The proposed methodology reveals the probability of insufficiency of the allocated capital to cover the commitments assumed by the insurer. In order to maintain resources to cover the indemnities payable to the insured, insurance companies include technical provisions in their balance sheets. Technical provisions are estimates and are therefore a source of fluctuations in the profit and loss statement of insurers, so understanding and protecting against these adverse variations is fundamental for efficient actuarial management. The stochastic approach enables internal models to be studied for solvency capital, which is a subject that lacks studies in the Brazilian market, and which is determined by a standard model pre-defined by the regulatory body. Stochastic modeling was proposed for Incurred But Not Reported Reserve using bootstrapping and, to validate this approach, the results were compared with the traditional approaches using real Motor Hull and Motor Third Part Liability data from a Brazilian insurance company. There are advantages of adopting stochastic methods instead of deterministic ones to determine technical provisions for claims, since it is possible to empirically estimate the probability distributions. The quantiles of these curves reveal the estimated probability of the real value exceeding a particular level of provisioning in order to extract the probability of capital shortage that the traditional methods do not provide. In addition, the results show that the traditional methods are too conservative, allocating more capital than necessary.

摘要：本文旨在通过确定性模型与随机性模型，获取可量化理赔技术准备金波动性的相关指标。简言之，传统精算方法未能提供的波动性测度与资本充足性缺口分析，对于高效精算管理而言具有核心重要性。本文提出的方法论可揭示保险公司为承担承保责任而拨付的资本出现缺口的概率。为覆盖向被保险人支付的赔款，保险公司需在资产负债表中计提技术准备金。技术准备金属于估算值，因此会成为保险公司损益表波动的来源，故而理解并对冲这类不利波动，是实现高效精算管理的核心要务。随机性方法可用于研究偿付能力资本的内部模型，这一主题在巴西保险市场尚缺乏相关研究，当前该类资本多由监管机构预先定义的标准模型确定。本文针对已发生未报案准备金（Incurred But Not Reported Reserve）提出了基于自举法（bootstrapping）的随机建模方案，并采用某巴西保险公司的真实机动车车身险与机动车第三者责任险业务数据，将该方法的结果与传统方法的结果进行对比以验证其有效性。相较于确定性方法，采用随机性方法确定理赔技术准备金具备诸多优势：其一，可通过实证方式估算概率分布。通过这些分布曲线的分位数，可测算实际赔款金额超出特定准备金计提水平的概率，进而获取传统方法无法提供的资本短缺概率。此外，研究结果表明，传统方法过于保守，会拨付超出实际所需的资本。