One-year estimation uncertainty in some claim development models

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

Following the works of Intergovernmental Panel on Climate Change (IPCC) in 2022, many climatologists have now accepted the notion of climate change. Despite all the research done, it is still a very complex concept to put into actionable models in the insurance industry. Such difficulty lies, among others, primarily in the short-time horizon that commercial companies contemplate. Typically, a business plan will not project any developments beyond a 5-year horizon, while climate change moves more slowly, where the IPCC typically looks at horizons of dozens of years. Through the application of Extreme Value Theory, this presentation intends to bridge the gap by attempting to see how the parameters of a Generalized Pareto Distribution (hereinafter “GPD”) fit into the estimated damage values of major catastrophes that evolve over the period of time 1946 – 2023. Based on the time dependency of the GPD parameters, this presentation will predict the exact year after which climate will become unpredictable and chaotic (see Smith (2003) and Bishop (2017)) hence bringing "the end of times”.

We introduce some deep learning models that simultaneously describe the dynamics of several yield curves. We aim to learn the dependence structure among the different yield curves induced by the globalization of financial markets and exploit it to produce more accurate forecasts. By combining the self-attention mechanism and nonparametric quantile regression, our model generates both point and interval forecasts of future yields. The architecture is designed to avoid quantile crossing issues affecting multiple quantile regression models. Numerical experiments conducted on two different datasets confirm the effectiveness of our approach. Finally, we explore potential extensions and enhancements by incorporating deep ensemble methods and transfer learning mechanisms.

Speaker: Salvatore Scognamiglio

Moderator: Brian Fannin