Quantitative Analysis of Insurance in the Financial Engineering Framework

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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.