Construction of suitable models for large-scale risks with application to non-life inssurance

2015 Fiscal Year Final Research Report

• Project/Area Number: 25870879
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Statistical science; Economic statistics
• Research Institution: Nanzan University
• Principal Investigator: MATSUI Muneya 南山大学, 経営学部, 准教授 (70449031)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: ポアソン・クラスターモデル / 確率過程の予測 / 損害保険モデル / 裾の厚い分布

Outline of Final Research Achievements

We extend a Poisson cluster model (PCM) in various ways so as to cope with different types of risks. The model has applications in the claims reserving problem in a non-life insurance context. Our versions could cope with extreme cases such that random components in the model may have no second moments. A crucial thing in applications is how we predict future risks based on the models cooperating with past observations. We establish effective numerical procedures for calculating predictors from observations. Moreover, we provide evaluation tools for prediction errors in a heavy tail case, which are given by fractional absolute moments.
Regarding one dimensional models, we obtain satisfactory results though there are some remaining things to do. Our next research step would be a spatial modeling of PCM, which enables better predictions of future risks.

Free Research Field

確率・統計