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Analytical calculation of risk measures for variable annuity guaranteed benefits

机译：可变年金保证利益的风险计量的分析计算

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With the increasing complexity of investment options in life insurance, more and more life insurers have adopted stochastic modeling methods for the assessment and management of insurance and financial risks. The most prevalent approach in market practice, Monte Carlo simulation, has been observed to be time consuming and sometimes extremely costly. In this paper we propose alternative analytical methods for the calculation of risk measures for variable annuity guaranteed benefits on a stand-alone basis. The techniques for analytical calculations are based on the study of geometric Brownian motion and its integral. Another novelty of the paper is to propose a quantitative model which assesses both market risk on the liability side and revenue risk on the asset side in the same framework from the viewpoint of risk management. As we demonstrate by numerous examples on quantile risk measure and conditional tail expectation, the methods and numerical algorithms developed in this paper appear to be both accurate and computationally efficient.
机译：随着人寿保险中投资选择的复杂性日益增加，越来越多的人寿保险公司采用随机建模方法来评估和管理保险及金融风险。市场实践中最普遍的方法，即蒙特卡洛模拟，被认为是耗时的，有时成本很高。在本文中，我们提出了单独计算可变年金担保收益风险度量的替代分析方法。分析计算技术基于对几何布朗运动及其积分的研究。本文的另一个新颖之处是提出了一种定量模型，该模型从风险管理的角度评估了在同一框架内的负债方的市场风险和资产方的收益风险。正如我们通过分位数风险度量和条件尾部期望的众多示例所证明的那样，本文开发的方法和数值算法似乎既准确又计算高效。

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