Statistics in Actuarial Science and Risk Management: Text Analysis, Sports Insurance, Privacy, and Structured Finance

In today's rapidly evolving AI landscape, advanced technologies such as Large Language Models (LLMs) present significant opportunities for transforming workers' compensation processes. This research leverages LLMs to analyze case records—often consisting of extensive textual data—and to predict the decision. By classifying and identifying nuanced patterns in these records, LLMs offer improved accuracy and efficiency compared to conventional analytic methods. The study addresses a critical gap in the workers' compensation domain, where comprehensive text analysis has historically been limited by the complexity and scale of available data. The research uses a publicly available dataset from the North Carolina Industrial Commission, wherein disputed workers' compensation claims are resolved through an administrative law process rather than traditional court litigation. The insights gained from this investigation have broad implications for actuaries, insurance companies, and legal professionals, highlighting how AI-driven techniques can streamline claims management, enhance predictive modeling, and contribute to fairer and more transparent outcomes. By demonstrating the utility of LLMs for classifying case decisions, this research underlines the transformative potential of AI in modernizing the workers' compensation sector. 

The guaranteed salaries of players in top professional leagues have grown substantially in recent years. Thus, the need for insurance policies that financially protect both teams and players in the event of injuries has become more commonplace. Despite the growing prevalence of such insurance products, there is a scarcity of actuarial analysis that assesses this risk. This study presents the first known actuarial analysis of player injuries and resulting claims severity through a compound risk model that separately analyzes injury frequency and claim severity. Our model incorporates covariate analysis using a comprehensive dataset that includes player biographies, player contracts, team travel, player performance, and player injury data. This method enables us to identify key risk factors influencing claim frequency and severity while suggesting premium models and potential risk mitigants. We first summarize this novel dataset of 508 players from the 2022-2023 NBA regular season with 640 unique injury details. We then discuss significant risk factors related to player injuries in the NBA. Consequently, we utilize the proposed premium pricing model to establish fair actuarial insurance rates for NBA players' sports injury insurance. Finally, we discuss the implications of our findings, including potential risk mitigation strategies and the long-term economic impact on player careers and league-wide financial stability. 

Microdata sharing is a common practice that enables various parties to benefit from the analysis of fine-grained information. However, it also poses a serious threat to the privacy of the individuals whose data are shared, as malicious actors may attempt to infer their sensitive attributes or identities from the shared data. To protect the privacy of the data subjects, data controllers often apply privacy-preserving techniques that introduce some distortion or noise to the original data, making it harder for an adversary to link them to specific individuals. However, these techniques also reduce the utility and accuracy of the data for legitimate analysis purposes. Therefore, a key challenge for data controllers is balancing the trade-off between privacy loss and data utility when choosing a suitable privacy-preserving technique. In this paper, we revisit a previously proposed method that allows partial recovery of the utility of randomized microdata by exploiting some auxiliary information. Based on this method, we propose a decision-making process that helps data controllers select the optimal differential privacy mechanism that minimizes privacy loss while meeting the utility requirement. 

The random cash flows of consumer auto asset-backed securities (ABS) depend critically on the time-to-event distribution of the individual, securitized assets. Estimating this distribution has historically been challenged by limited data. Recent regulatory changes reversed this, however, and asset-level auto ABS data is now publicly available to investors for the first time. The idiosyncrasies of this ABS data present new difficulties in estimating the loan-level lifetime distribution due to its discrete-time structure, finite support, and exposure to left-truncation. We propose a parametric framework for estimating the loan-level lifetime distribution while leaving the left-truncation time distribution unspecified. Through theorems developed to identify the stationary points of the likelihood, we significantly simplify a complex multiparameter constrained optimization problem. These stationary points, shown to be the roots of an estimating equation, enable asymptotic normality and large-sample inference to follow. In the special case of a finite geometric distribution via an actuarial policy limit, closed-form maximum likelihood estimates may be derived. These theoretical results are further generalized to accommodate right-censoring and validated through numerical and simulation studies. These efficient and accurate estimation methods are then applied to data from two Ally Auto Receivables Trust ABS bonds, which can offer potentially valuable insights to investors.