arXiv subjects

Tsz Chai Fung

Publications and source records attributed to Tsz Chai Fung.

9 recordsLinked to original sources

arXiv2026

Quantifying Social Inflation in Liability Insurance with Advanced Statistical Methods

Social inflation, which is the rise in liability claim costs beyond general economic inflation, has become a major concern for insurers and reinsurers, yet it is difficult to quantify because litigation outcomes are heavy-tailed and the mix of cases reaching verdict versus settlement changes over time. Using a large database of US jury verdicts and settlements, we develop case-mix-adjusted social inflation measures through multiple channels that matter to reinsurers: plaintiff win rates (a frequency-type channel), settlement propensity (a frequency-type channel), and verdict/settlement severity. The approach combines rolling-window logistic regression for probabilities and quantile (value-at-risk) regression for severities, with uncertainty quantified via a random-weighted bootstrap. We find statistically significant relative increases in plaintiff win probability of approximately 20%-30% from 2009 to 2024, alongside a statistically significant relative decline in settlement probability of more than 10% over the same period. The dominant channel is verdict severity: Even after controlling for explanatory variables, verdict awards show a sharp rise after 2020, increasing by more than 100% from 2020 to 2024, whereas settlement amounts show limited and often statistically insignificant inflation. Therefore, inflation in total amounts payable to plaintiffs closely tracks verdict severity. Social inflation is more pronounced in corporate-defendant and uninsured-defendant cases and in states without tort caps or third-party litigation funding regulation. In addition, we find that social inflation has impacts not only on "nuclear verdicts" but also, in a similar manner, on moderate losses.

econ.GN↗

arXiv2025

Statistical Learning of Trade Credit Insurance Network Data with Applications to Ratemaking and Reserving

Trade credit insurance (TCI) is a specialized line of property and casualty insurance, protecting businesses against financial losses due to buyer's insolvency. Predictive modeling for TCI claims poses formidable challenges due to the data's complexity, yet remains underexplored in the literature. Leveraging six years of detailed TCI data from an Asian TCI insurer, we develop a bivariate, network-augmented Generalized Linear Mixed Model (GLMM) to jointly model claim probability and reporting time gaps. Our model integrates extended-order degree centrality and random effects at the business and policy levels, adjusted for data incompleteness, to capture claim histories, reporting time gaps, and network relationships specific to TCI data. To implement a feasible workaround for the high-dimensional integrations required by individual random effects, we propose a scalable Stochastic Expectation-Maximization (SEM) algorithm. Data analysis using this TCI dataset demonstrates that our model significantly outperforms benchmark models in both model fit and predictive accuracy, highlighting the effectiveness of our approach for improved ratemaking and reserving in TCI. Supplementary materials for this article are available as an online supplement.

stat.AP↗

arXiv2024

A Revisit of the Optimal Excess-of-Loss Contract

It is well-known that Excess-of-Loss reinsurance has more marketability than Stop-Loss reinsurance, though Stop-Loss reinsurance is the most prominent setting discussed in the optimal (re)insurance design literature. We point out that optimal reinsurance policy under Stop-Loss leads to a zero insolvency probability, which motivates our paper. We provide a remedy to this peculiar property of the optimal Stop-Loss reinsurance contract by investigating the optimal Excess-of-Loss reinsurance contract instead. We also provide estimators for the optimal Excess-of-Loss and Stop-Loss contracts and investigate their statistical properties under many premium principle assumptions and various risk preferences, which according to our knowledge, have never been investigated in the literature. Simulated data and real-life data are used to illustrate our main theoretical findings.

stat.AP↗

arXiv2023

Diagnostic Tests Before Modeling Longitudinal Actuarial Data

In non-life insurance, it is essential to understand the serial dynamics and dependence structure of the longitudinal insurance data before using them. Existing actuarial literature primarily focuses on modeling, which typically assumes a lack of serial dynamics and a pre-specified dependence structure of claims across multiple years. To fill in the research gap, we develop two diagnostic tests, namely the serial dynamic test and correlation test, to assess the appropriateness of these assumptions and provide justifiable modeling directions. The tests involve the following ingredients: i) computing the change of the cross-sectional estimated parameters under a logistic regression model and the empirical residual correlations of the claim occurrence indicators across time, which serve as the indications to detect serial dynamics; ii) quantifying estimation uncertainty using the randomly weighted bootstrap approach; iii) developing asymptotic theories to construct proper test statistics. The proposed tests are examined by simulated data and applied to two non-life insurance datasets, revealing that the two datasets behave differently.

stat.ME↗

arXiv2022

Mixture of experts models for multilevel data: modelling framework and approximation theory

Multilevel data are prevalent in many real-world applications. However, it remains an open research problem to identify and justify a class of models that flexibly capture a wide range of multilevel data. Motivated by the versatility of the mixture of experts (MoE) models in fitting regression data, in this article we extend upon the MoE and study a class of mixed MoE (MMoE) models for multilevel data. Under some regularity conditions, we prove that the MMoE is dense in the space of any continuous mixed effects models in the sense of weak convergence. As a result, the MMoE has a potential to accurately resemble almost all characteristics inherited in multilevel data, including the marginal distributions, dependence structures, regression links, random intercepts and random slopes. In a particular case where the multilevel data is hierarchical, we further show that a nested version of the MMoE universally approximates a broad range of dependence structures of the random effects among different factor levels.

math.ST↗

arXiv2022

A Posteriori Risk Classification and Ratemaking with Random Effects in the Mixture-of-Experts Model

A well-designed framework for risk classification and ratemaking in automobile insurance is key to insurers' profitability and risk management, while also ensuring that policyholders are charged a fair premium according to their risk profile. In this paper, we propose to adapt a flexible regression model, called the Mixed LRMoE, to the problem of a posteriori risk classification and ratemaking, where policyholder-level random effects are incorporated to better infer their risk profile reflected by the claim history. We also develop a stochastic variational Expectation-Conditional-Maximization algorithm for estimating model parameters and inferring the posterior distribution of random effects, which is numerically efficient and scalable to large insurance portfolios. We then apply the Mixed LRMoE model to a real, multiyear automobile insurance dataset, where the proposed framework is shown to offer better fit to data and produce posterior premium which accurately reflects policyholders' claim history.

stat.AP↗

arXiv2022

Robust estimation and model diagnostic of insurance loss data: a weighted likelihood approach

This paper presents a score-based weighted likelihood estimator (SWLE) for robust estimations of generalized linear model (GLM) for insurance loss data. The SWLE exhibits a limited sensitivity to the outliers, theoretically justifying its robustness against model contaminations. Also, with the specially designed weight function to effectively diminish the contributions of extreme losses to the GLM parameter estimations, most statistical quantities can still be derived analytically, minimizing the computational burden for parameter calibrations. Apart from robust estimations, the SWLE can also act as a quantitative diagnostic tool to detect outliers and systematic model misspecifications. Motivated by the coverage modifications which make insurance losses often random censored and truncated, the SWLE is extended to accommodate censored and truncated data. We exemplify the SWLE on three simulation studies and two real insurance datasets. Empirical results suggest that the SWLE produces more reliable parameter estimates than the MLE if outliers contaminate the dataset. The SWLE diagnostic tool also successfully detects any systematic model misspecifications with high power, accompanying some potential model improvements.

stat.ME↗

arXiv2021

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 the tail part of FMM. With a probabilistic interpretation for MWLE, Generalized Expectation-Maximization (GEM) algorithm is still applicable for efficient parameter estimations. We therefore present and compare two distinctive constructions of complete data to implement the GEM algorithm. By exemplifying our approach on two simulation studies and a real motor insurance data set, we show that comparing to MLE, MWLE produces more appropriate estimations on the tail part of FMM, without much sacrificing the flexibility of FMM in capturing the body part.

stat.ME↗

arXiv2021

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 which significantly impact the mixing probabilities and the different mixture components, respectively. We develop an asymptotic theory for this regularized estimation approach, and fitting is performed using a novel Generalized Expectation-Maximization algorithm. We exemplify our approach on real motor insurance data set.

stat.ME↗