CAS Research Papers and Briefs

CAS Research Papers are funded, peer-reviewed, in-depth works focusing on important topics within property-casualty actuarial practice. Funding for CAS Research Papers comes from CAS member dues, individual grants and other sources. Topics are solicited through a variety of means including CAS committees and formal requests for proposals.

CAS Research Papers fulfill the goal of creating an important addition to the existing body of CAS literature and give CAS members access to relevant information and resources applicable to their work, which can help advance their careers.

Research Papers

Social Inflation and Loss Development — An Update

By Jim Lynch, FCAS, MAAA, and Dave Moore, FCAS, CERA

In a previous CAS Research Paper, we described a method for using industrywide loss development factors to detect circumstances consistent with descriptions of a phenomenon known as social inflation. The paper focused primarily on commercial auto liability insurance as defined in Schedule P of the Annual Statement. We estimated that social inflation increased commercial auto liability claims by more than $20 billion between 2010 and 2019. This paper extends our analyses through the end of 2021, focusing again on commercial auto liability. We find that one metric for detecting excessive claims inflation, the calendar year 12–60-month loss development factor (abbreviated as the CYR 12-60 LDF) decreased significantly after calendar year 2019. The 2020 and 2021 factors were at levels consistent with 2016 and 2017. We believe the decrease was driven primarily by the pandemic, in part, due to slowdowns in tort dispositions and backlogs in cases. That the CYR 12-60 LDF remained significantly higher than a decade earlier is evidence that a certain level of social inflation remains baked into industry results, even in 2020 and 2021. We estimate that social inflation increased commercial auto liability estimates by more than $30 billion between 2012 and 2021, with most of the increase coming from the addition of 2020 and 2021 to the analysis.

Sponsored by the Insurance Information Institute and the Casualty Actuarial Society

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Understanding the Demand for Inclusive Insurance: A Pilot Study

By Ida Ferrara, Edward Furman, Tsvetanka Karagyozova

The goal of this study is to pave the way for a more comprehensive assessment of the potential benefit of microinsurance (MI) to low-income households in any country, regardless of its level of development, by piloting and implementing a survey instrument to enhance our understanding of the drivers of risk- and insurance-related decisions pertaining to the purchase of health, life and property insurance. For the purposes of the paper, the authors take MI to refer to the provision of conventional insurance products with small limits and simple coverages to low-income individuals.

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Climate, Spatial Dependence, and Flood Risk: A U.S. Case Study

By Robert J. Erhardt, ACAS; Mathieu Boudreault; David A. Carozza; and Kejia Yu

Flood represents one of the costliest and most disruptive natural disasters in the United States, and the economic losses from flooding are trending upward. While this trend is known to be driven primarily by an increasing population and wealth exposure, climate change is also affecting flood risk in more subtle ways. The authors merge data on economic flood losses, historical climate, census population, and geological characteristics to explore drivers of flood losses and climate trends. The data cover 292 watersheds spanning the continental United States, over the period 1979–2018. The authors fit a Bayesian spatial mixed-effects model for flood loss frequency and a Bayesian mixed effects model for flood severity loss per person. Both models control for measured covariates, contain random effects to capture variation from unmeasured covariates, and quantify climate drivers of flood risk.

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Spatial-Temporal Modeling of Wildfire Losses with Applications in Insurance-Linked Securities Pricing

By Hong Li and Jianxi Su

In this project, the authors model and predict state-specific wildfire losses in the United States using a combination of Bayesian dynamic models. In particular, the wildfire frequencies are modeled by a Bayesian multi-scale Dynamic Count Mixture Model (DCMM), which is capable of capturing a number of stylized features of wildfire data, including zero-inflation, over-dispersion compared to the Poisson distribution, and the time-varying patterns. Further, the DCMM is able to incorporate spatial dependence of different states, and thus improves the forecasting performance for individual states, especially those with low historical frequencies. The authors then apply the predictive distribution of future wildfire loss to price wildfire catastrophe (CAT) bonds with different characteristics and evaluate their hedging effectiveness for insurers in different states.

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Social Inflation and Loss Development

By Jim Lynch, FCAS, MAAA, and Dave Moore, FCAS, CERA

The phenomenon of social inflation has garnered a great deal of attention in the property and casualty (P&C) insurance industry. The term defies strict definition, though it is widely acknowledged to involve excessive growth in insurance settlements. We examine evidence for its existence in standard industrywide claims triangles through 2019. The focus is on commercial automobile liability insurance, though other annual statement lines of business are examined as well. We find development patterns in commercial auto liability are consistent with most descriptions of social inflation. We estimate that social inflation increased commercial auto liability claims by more than $20 billion between 2010 and 2019. Evidence of a similar trend is also present in two other lines of business: other liability—occurrence and medical malpractice—claims made. We also use standard actuarial metrics and visualizations to demonstrate how actuarial insights can be presented to an interested lay audience, such as lawmakers, regulators, the news media, and the public.

Sponsored by the Insurance Information Institute and the Casualty Actuarial Society

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Individual Claims Forecasting with Bayesian Mixture Density Networks

By Kevin Kuo

This paper introduces an individual claims forecasting framework utilizing Bayesian mixture density networks that can be used for claims analytics tasks such as case reserving and claims triaging. This approach produces multi-period, cash-flow forecasts. The modeling framework uses a publicly available data simulation tool.

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Exposure Measures for Pricing and Analyzing the Risks in Cyber Insurance

By Michael A. Bean, FCAS, CERA, FCIA, FSA, Ph.D.

Although available since the 1990s, cyber insurance is still a relatively new product that is ever-changing. The report uses a conceptual approach to identify and evaluate potential exposure measures for cyber insurance. In particular, the report studies the losses that can arise with each cyber insurance coverage and identifies potential exposure measures related to these losses. The report then evaluates these potential exposure measures based on a set of criteria, which include ease of calculation, ability to audit the calculation, strength of relationship to losses, and stability over the period of insurance coverage as well as concerns over privacy laws and regulatory requirements.

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Hierarchical Compartmental Reserving Models

By Markus Gesmann and Jake Morris

Hierarchical compartmental reserving models give a parametric framework to describe aggregate insurance claims processes using differential equations. The paper discusses how these models can be specified in a fully Bayesian modeling framework to jointly fit paid and outstanding claims development data; demonstrates how modelers can utilize their expertise to describe specific development features and incorporate prior knowledge into parameter estimation; explores subtle yet important differences between modeling incremental and cumulative claims payments; examines parameter variation across multiple dimensions; and introduces an approach to incorporate market cycle data into the modeling process. Examples and case studies are shown using Stan via the brms package in R.

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A User’s Guide to Economic Scenario Generation in Property/Casualty Insurance

By Conning

This paper serves as a basic guide to economic scenario generators (ESGs), with an emphasis on applications for the property-casualty insurance industry. An ESG is a computer-based model that provides simulated examples of possible future values of various economic and financial variables. The paper provides general information on the nature of ESGs, discusses essential features of a good one, and provides guidance on stochastic processes and modeling of certain economic and financial variables. The importance of financial market model specification, model calibration, and model validation are discussed. This assures that the ESG will produce simulation results that are relevant and sufficiently robust and that will realistically reflect market dynamics. The paper also provides a concrete illustration which describes issues and decisions made in constructing and using a specific ESG.  Considerations relating to the projection time frame are explored in depth. Finally, a discussion of the range of choices for software in developing ESGs is presented, contrasting open-source ESGs with solutions that are available from commercial vendors.

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Catastrophe Models for Wildfire Mitigation: Quantifying Credits and Benefits to Homeowners and Communities

By CAS, CoreLogic, Milliman

Unprecedented costs from wildfires in the American West have spurred a need for wildfire risk reduction in at-risk areas; meanwhile, communities and homeowners need tools to understand the costs and benefits of various means of wildfire risk mitigation. Appropriate quantification of the impacts of various mitigation efforts (such as mitigation premium credits) can benefit both insurers and consumers, as well as inform public policy and public safety decisions. This paper explores the need for catastrophe models to perform the quantification of mitigation efforts, outlines actuarial considerations and approaches for developing wildfire mitigation premium credits, and describes challenges in obtaining data and implementing mitigation premium credits. The paper illustrates these concepts through a detailed case study based on a specific community representing a significant concentration of wildfire risk in Northern California.

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Assessing the Impact of Marijuana Decriminalization on Vehicle Accident Experience

By CAS and Canadian Institute of Actuaries

This report by the Canadian Institute of Actuaries (CIA) and Casualty Actuarial Society (CAS) contains analysis of the impact of marijuana decriminalization on vehicle accident experience. This report utilizes technical advancements of machine learning algorithms for finding patterns in data, rigorous approaches for selecting control units from observational data, and recently developed pathways for a causal interpretation of black-box models. Canadian and US data for 2016–2019 were used in the study, including official reports on collisions of private vehicles and losses in Canada, fatal accidents, and weather factors in the United States. For each data source, statistical and machine learning models were chosen to account for different sources of variability.

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Research Briefs

COVID-19: The Property-Casualty Perspective

By Brian Fannin
The world is going through an extraordinary event. Since it first appeared in Wuhan, China, in late 2019 (“First Covid-19 Case Happened in November, China Government Records Show - Report” 2020), the coronavirus has spread rapidly to most of the world’s population. Indeed, one of the difficulties of writing an article like this is to keep up with the pace of change. An earlier draft had included specific references to the current number of countries and individuals who had been affected. It took only a few days for those numbers to be badly short of the mark.

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On Insurability and Transfer of Pandemic Business Interruption Risk

By Aditya Khanna, FCAS; Brian A. Fannin, ACAS, CSPA; and Tim Wei, FCAS

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Series on Race and Insurance Pricing
The Casualty Actuarial Society is committed to diversity, equity and inclusion in all aspects of actuarial work and has produced four CAS Research Papers to help guide the insurance industry toward proactive, quantitative solutions to address potential racial bias in insurance pricing. Through these research papers, we aim to inspire and generate discussions about potential racial bias across all areas of insurance pricing and to encourage actuaries to lead the conversations with other stakeholders on this topic.
cyber risk
Catastrophic Cyber Risk: An Expert Panel Discussion Series