Dependencies in Stochastic Loss Reserve Models

With the advancement of technology, insurance companies are increasingly adopting usage-based insurance (UBI) supported by vehicle telematics. Vehicle telematics refers to data collected from in-vehicle sensors or smartphone applications during driving, such as speed, acceleration, braking, and steering. It provides a rich, high-frequency record of how a vehicle is driven, offering insights into driving habits, behaviour, safety, and potential risk. However, many current approaches rely on aggregated metrics and do not fully capture the detailed time-series patterns in telematics data. This presentation introduces a flexible framework based on a continuous-time hidden Markov model (CTHMM) to analyze trip-level telematics data directly. Our approach avoids predefined thresholds for harsh events or assumptions about accident probabilities, and uses only telematics data, requiring no traditional demographic covariates. Using an unsupervised anomaly detection technique, we identify deviations from normal driving patterns linked to higher accident risk. The framework is tested on both controlled and real-world datasets, and the results reveal clear behavioural differences between drivers with and without claims, offering practical insights for insurance, accident analysis, and prevention.

This session brings together actuarial and machine learning perspectives to explore how AI can support reserving practices.

The actuarial perspective will cover the practical limitations of current reserving workflows, where judgment enters traditional methods and why consistency is difficult, and what actuaries need from AI, including transparency, validation, and governance. It will also include a case study comparing traditional results with AI-supported modeling and how ML results can serve as a second-opinion framework.

The machine learning perspective will cover the Bayesian ML framework, including its architecture, model selection based on predictive power and cross-validation, and how explainability is built into the model. It will also discuss why full distributions matter more than point estimates and share technical lessons from applying ML to insurance triangles.

Speakers: Ben Zickel and Yulia Nechay Moderator: Joana Raposo

This webinar explores the evolving cyber threat landscape, and the steps organizations can take to build resilience.

Drawing on insights from simulated sophisticated cyberattacks, we will share key lessons learned, highlight the most common pitfalls that leave businesses vulnerable, and provide actionable recommendations to reduce risk.

Framed in the context of current and emerging threats including ransomware, AI-driven attacks, and supply-chain vulnerabilities, this session aims to equip decision-makers with clear strategies to strengthen defenses, improve response readiness, and ensure business continuity in the face of an increasingly hostile digital environment.

The additive reserving model assumes the existence of volume measures such that the corresponding expected loss ratios are identical for all accident years. While classical literature assumes these volumes are known, in practice, accurate volume measures are often unavailable. The issue of uncertain volume measures in the additive model was addressed in a generalization of the loss ratio method published in 2018. The derivation is rather complex and the method computationally intensive, especially for large loss development triangles.
We present an alternative approach that leverages the well-established EM algorithm, significantly reducing computational requirements.


Speaker: Ulrich Riegel
Session moderator: Brian Fannin

This talk presents a method for constructing insurable risk portfolios using a data-driven approach to devise risk retention programs that safeguard firms from a multitude of risks. Because firms face many risks, including fire damage to their buildings, liability from management misconduct, and external threats like cyber attacks, this talk treats these potential liabilities as a "portfolio." Drawing inspiration from Markowitz portfolio theory, it leverages techniques from probability, statistics, and optimization to build algorithms that construct optimal risk insurable portfolios under budget constraints. Through engaging case studies, viewers will learn how to build optimal insurable risk portfolios.
The talk illustrates a frontier that depicts the trade-off between the uncertainty of a portfolio and the cost of risk transfer. This visual representation, mirroring familiar Markowitz investment tools, enables informed decision-making and easy adoption by risk advisors. The talk outlines the mathematical groundwork for constructing optimal insurable risk portfolios in an effective and aesthetically pleasing manner.

Speaker: Edward (Jed) Frees
Moderator: Brian Fannin

In this session we explore how the localized nature of severe weather events leads to a concentration of correlated risks that can substantially amplify aggregate losses. We propose a copula-based regression model for replicated spatial data to characterize the dependence between property damage claims from a common storm. The factor copula captures spatial dependence between properties and aspatial dependence induced by the common shock. The framework allows insurers to incorporate heterogeneity in marginal models of skewed, heavy-tailed, and zero-inflated insurance losses, while retaining model interpretation. Using hail damage insurance claims data from a US insurer, we demonstrate the effect of dependence on claims management decisions.


Speaker: Lisa Gao
Session moderator: Brian Fannin