Alternative modelling and inference methods for claim size distributions

Multi-Parameter Regression Survival Modelling: An Alternative to Proportional Hazards

It is standard practice for covariates to enter a parametric model through a single distributional parameter of interest, for example, the scale parameter in many standard survival models. Indeed, the well-known proportional hazards model is of this kind. In this paper we discuss a more general approach whereby covariates enter the model through more than one distributional parameter simultaneously (e.g., scale and shape parameters). We refer to this practice as "multi-parameter regression" (MPR) modelling and explore its use in a survival analysis context. We find that multi-parameter regress…

Mixture composite regression models with multi-type feature selection

The aim of this paper is to present a mixture composite regression model for claim severity modelling. Claim severity modelling poses several challenges such as multimodality, heavy-tailedness and systematic effects in data. We tackle this modelling problem by studying a mixture composite regression model for simultaneous modeling of attritional and large claims, and for considering systematic effects in both the mixture components as well as the mixing probabilities. For model fitting, we present a group-fused regularization approach that allows us for selecting the explanatory variables whic…

用于损失准备金评估的贝叶斯偏态重尾建模

A Bayesian Skew-heavy-tailed modelling for loss reserving

针对未决赔款金额不确定且数据常呈偏态重尾的问题，提出贝叶斯偏态重尾损失准备金模型，并用自适应 Metropolis 步骤的 MCMC 推断，案例表明其优于传统模型。

Modelling excess zeros in count data: A new perspective on modelling approaches

We consider the analysis of count data in which the observed frequency of zero counts is unusually large, typically with respect to the Poisson distribution. We focus on two alternative modelling approaches: Over-Dispersion (OD) models, and Zero-Inflation (ZI) models, both of which can be seen as generalisations of the Poisson distribution; we refer to these as Implicit and Explicit ZI models, respectively. Although sometimes seen as competing approaches, they can be complementary; OD is a consequence of ZI modelling, and ZI is a by-product of OD modelling. The central objective in such analys…

使用贝叶斯隐马尔可夫模型联合估计保险损失进展因子

Joint estimation of insurance loss development factors using Bayesian hidden Markov models

本文提出用贝叶斯隐马尔可夫模型联合估计保险损失进展中的主体链接比率和尾部因子，通过自动学习潜在状态克服传统两步法的主观偏差，并在数值与行业数据上取得更优表现。

Estimation of foreseeable and unforeseeable risks in motor insurance

This project works with the risk model developed by Li et al. (2015) and quests modelling, estimating and pricing insurance for risks brought in by innovative technologies, or other emerging or latent risks. The model considers two different risk streams that arise together, however not clearly separated or observed. Specifically, we consider a risk surplus process where premia are adjusted according to past claim frequencies, like in a Bonus-Malus (BM) system, when we consider a classical or historical risk stream and an unforeseeable risk one. These are unknown risks which can be of high unc…

Model Averaging based Semiparametric Modelling for Conditional Quantile Prediction

In real data analysis, the underlying model is usually unknown, modelling strategy plays a key role in the success of data analysis. Stimulated by the idea of model averaging, we propose a novel semiparametric modelling strategy for conditional quantile prediction, without assuming the underlying model is any specific parametric or semiparametric model. Thanks the optimality of the selected weights by cross-validation, the proposed modelling strategy results in a more accurate prediction than that based on some commonly used semiparametric models, such as the varying coefficient models and add…

Maximum weighted likelihood estimator for robust heavy-tail modelling of finite mixture models

In this article, we present the maximum weighted likelihood estimator (MWLE) for robust estimations of heavy-tail finite mixture models (FMM). This is motivated by the complex distributional phenomena of insurance claim severity data, where flexible density estimation tools such as FMM are needed but MLE often produces unstable tail estimates under FMM. Under some regularity conditions, MWLE is proved to be consistent and asymptotically normal. We further prove that the tail index obtained by MWLE is consistent even if the model is misspecified, justifying the robustness of MWLE in estimating …

左截断健康保险理赔数据：理论综述与实证应用

Left-Truncated Health Insurance Claims Data: Theoretical Review and Empirical Application

本研究基于AOK的25万左截断健康保险理赔数据，通过条件似然与Jacod公式分析中风对痴呆发病的影响，发现中风后痴呆发病强度显著上升，年龄非齐次模型下效应减半，调整多病共存后无进一步变化。

A general framework for modelling zero inflation

We propose a new framework for the modelling of count data exhibiting zero inflation (ZI). The main part of this framework includes a new and more general parameterisation for ZI models which naturally includes both over- and under-inflation. It further sheds new theoretical light on modelling and inference and permits a simpler alternative, which we term as multiplicative, in contrast to the dominant mixture and hurdle models. Our approach gives the statistician access to new types of ZI of which mixture and hurdle are special cases. We outline a simple parameterised modelling approach which …

Assessing an Alternative for `Negative Variance Components': A Gentle Introduction to Bayesian Covariance Structure Modelling for Negative Associations Among Patients with Personalized Treatments

The multilevel model (MLM) is the popular approach to describe dependences of hierarchically clustered observations. A main feature is the capability to estimate (cluster-specific) random effect parameters, while their distribution describes the variation across clusters. However, the MLM can only model positive associations among clustered observations, and it is not suitable for small sample sizes. The limitation of the MLM becomes apparent when estimation methods produce negative estimates for random effect variances, which can be seen as an indication that observations are negatively corre…

概率建模足以进行因果推断

Probabilistic Modelling is Sufficient for Causal Inference

本文表明，概率建模足以回答因果推断问题，无需专门的因果工具或符号。

基于Kumaraswamy密度加权的索赔严重性模型的$L$-估计

$L$-estimation of Claim Severity Models Weighted by Kumaraswamy Density

针对保险索赔严重性建模中传统L估计量加权方案僵化的问题，提出Kumaraswamy密度加权的灵活稳健L估计框架，经理论证明和实验验证，在处理异常值与重尾分布时性能优于传统方法。