Quantitative Analysis of Insurance in the Financial Engineering Framework

本研究是在2004-2006财政年度进行的，研究内容如下：A)死亡率风险及其统计模型为了管理养老金计划中的寿命风险，我们研究了未来死亡率的几种统计模型。我们特别关注Lee-Carter方法，并将其泊松回归版本应用于日本死亡率数据。2005年，我们提出了一种基于局部似然技术的平滑形式的Lee-Carter模型。2006年，我们进一步扩展了该模型，将其置于贝叶斯框架中。B)多元风险中性概率的校准面对金融与保险的转换，需要对股票指数年金等依赖于多种资产的产品进行风险评估。我们对“共构性”这一新概念进行了基础性研究，以期对亚洲和篮子型期权进行定价。注意到多元风险中性分布可以分解为边际分布和联结分布，我们提出了一种新的校正方法，即用对数正态混合分布建模边际分布，用失真法建模联结分布。c)发展基于局部矩的非参数方法在许多实际情况下，数据在统计分析之前以局部矩和百分位数等汇总形式呈现。我们为这种聚合数据开发了非参数技术。在2004年，我们考虑了基于局部矩的最大似然估计。2005年，我们开始研究数据压缩（一种用于海量数据集的数据挖掘技术）与核密度估计之间的联系，并于2006年提出了一种称为核数据压缩的数据压缩技术。

The research was conducted over the fiscal years 2004-2006 as follows:A)Mortality risk and its statistical modelingToward managing the longevity risk in pension plans, we examined several statistical modeling for the future mortality rates. In particular, we focused on the Lee-Carter methodology and applied its Poisson regression version to the Japanese mortality data. In the year 2005 we proposed a smoothed form of the Lee-Carter model based on the local likelihood technique. In the year 2006 we further extended the model by setting it in a Bayesian framework.B)Calibration of multivariate risk neutral probabilityIn the face of the conversion of the finance and insurance, the risk valuation for products dependent on multiple assets, such as equity indexed annuity, is in the need. We made a fundamental study into the new concept "comonotonicity" with a view to pricing the Asian-and basket-type options. Noting that the multivariate risk neutral distribution can be decomposed into the marginal distributions and the copula, we propose a new calibration method which models the marginal distribution by a log normal mixture distribution and the copula by a distortion method.C)Developing the nonparametric method based on local momentsFor many practical situations data are presented in aggregated forms such as local moments and percentiles prior to statistical analyses. We developed nonparametric techniques for such aggregated data. In the year 2004 we considered the maximum likelihood estimation based on the local moments. In the year 2005 we started to investigate the connection between the data squashing-a data mining technique for massive data sets and the kernel density estimation and proposed a data compression technique called a kernel data squashing in the year 2006.