Panel Count Data with Dynamic Random Effects in Actuarial Sciences

精算科学中具有动态随机效应的面板计数数据

• 批准号: 356489-2013
• 负责人: Boucher, JeanPhilippe
• 金额: $ 0.8万
• 依托单位: Université du Québec à Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635753
• 关键词: Panel; Count; Data; Dynamic; Random

My research program is about mathematical developments for general insurance (Fire, Accident & Casualty). The main idea is to model the number of claims to an insurer where the dependence between all the contracts of the same insured, called panel data structure, will be put forward in the modeling. To do this, the research program is divided into two independent axes:1. A theoretical approach that requires new statistical developments on time series for count, before the preliminary application to real data panel. Various forms of conditional distributions (such as hurdle or zero-inflated models) will be tested, and various forms of the underlying dynamic process will also be verified (generalization of the multifractal models with a larger number of fractal processes, or using other forms of processes). New estimation techniques and new time series models will be used and generalized, such as filtering techniques, like particle filter approximation or a linear Kalman filter, for example. Because of their high speed, multifractal models can also be used in some importance sampling methods.2. A practical approach based on bonus-malus systems (BMS) where, instead of working with an advanced statistical model that creates time dependence between all the contracts of the same insured, we assume that a BMS plays this role. In this innovative approach, a new criterion is proposed based on a competitive angle. Indeed, the insurer must offer a premium high enough to cover the risk, but lower than that of the competitors. We will select the best BMS on this criterion instead of using classic information criterion based on log-likelihood statistics.

我的研究计划是关于一般保险（火灾，事故和伤亡）的数学发展。主要思想是将索赔数量建模到保险公司，其中同一被保险人的所有合同（称为面板数据结构）将在模型中提出。为此，研究计划分为两个独立的轴：1。一种理论方法，需要在对真实数据面板进行初步应用之前，需要在计数时间序列上进行新的统计发展。将测试各种形式的条件分布（例如障碍物或零膨胀模型），并且还将验证各种形式的基本动态过程（对具有较大分形过程的多型模型的概括，或使用其他形式的过程）。例如，将使用和广泛化新的估计技术和新的时间序列模型，例如过滤技术，例如粒子滤波器近似或线性卡尔曼滤波器。由于它们的高速，多型模型也可以用于某种重要的采样方法中。2。一种基于奖励 - 麦卢斯系统（BMS）的实用方法，在该方法中，我们假设A BMS扮演该角色，而不是使用高级统计模型，而不是与高级统计模型一起创建时间依赖性。在这种创新的方法中，基于竞争角度提出了一个新标准。确实，保险公司必须提供足够高的溢价来承担风险，但低于竞争对手。我们将在此标准上选择最佳的BMS，而不是基于日志类统计的经典信息标准。