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### 基于GB2分布的贝叶斯相依性准备金评估模型

• 出版日期:2018-01-25 发布日期:2018-01-25

### Bayesian Dependent Loss Reserving Models Based on GB2 Distribution

Li Zhengxiao & Meng Shengwang

• Online:2018-01-25 Published:2018-01-25

Abstract: One of the most critical problems in casualty insurance is to determine an appropriate outstanding reserve for incurred but unpaid losses. Forecasts and risk margins are often based on incremental or cumulative payment data corresponding to different business lines of loss triangles. Modeling dependency among multiple loss triangles has important implication for the determination of loss reserves in property and casualty insurance. In fact, owing to diversity of loss reserving data, it is critical to select the appropriate distribution. Generalized beta distribution of the second kind (GB2 distribution) has a flexible probability density function with four parameters, which nests various distributions with light and heavy tails, to facilitate accurate loss reserving in insurance applications. This paper proposes a Bayesian model based on GB2 distribution to capture dependence between two cells of two different runoff triangles. First, we use the GB2 distribution to fit the incremental paid losses data and introduce accident year and development year as covariates. Then, we suppose a dependence between all the observations that belong to the same calendar year (CY) for each line of business. This model can be done by using the calendar year as common random effect. For illustration, the model is applied to a dataset from Shi (2011) where a Bayesian method is proposed to estimate the distribution of the reserve. The result shows that the proposed model is more fully considered for the tail risk and uncertainty of the outstanding reserve than existing models, and is more suitable to model the loss reserving data with long and heavy tails.