The distribution function of the sum of dependent risks: a geometric-combinatorial approach

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

In this webinar, we explore a non-cooperative optimal reinsurance problem under likelihood ratio uncertainty, aiming to minimize the insurer's worst-case retained loss. We relate the optimal reinsurance strategy under the reference measure to that in the worst-case scenario, with generalizations to insurance design problems using tail risk measures. We also identify distortion risk measures where the insurer’s optimal strategy remains unchanged in the worst-case. Using an expectile risk measure, we determine optimal policies for the worst-case. Additionally, we examine a cooperative problem as a general risk-sharing model between two agents in a comonotonic market, comparing outcomes with the non-cooperative case.


Speaker: Ziyue Shi
Moderator: Brian Fannin