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
By Jim Lynch, FCAS, MAAA, Dave Moore, FCAS, MAAA, William Nibbelin and Dale Porfilio, FCAS, MAAA
This study, jointly sponsored by the Casualty Actuarial Society and the Insurance Information Institute, assesses the impact of combined social and economic inflation on auto liability insurance through year-end 2023. Social inflation, which refers to the excessive growth in claims costs, and economic inflation have driven significant increases in insurance losses. The paper evaluates these effects using actuarial methods, such as analyzing loss development factors (LDFs), which track how loss estimates evolve over time, and comparing actual vs. expected loss emergence. Trends in claim frequency and severity are also examined, revealing how changes in the number of claims and their average costs contribute to overall inflationary pressures.
As digital assets continue to reshape finance, so must cyber insurers protect customers at both micro and systematic levels. “A Framework for Digital Asset Risks with Insurance Applications,” released by the Casualty Actuarial Society and Society of Actuaries, provides actuaries a foundation for safeguarding the integrity and stability of the rapidly evolving digit asset landscape.
Besides offering a scientifically rigorous framework for quantifying cyber risks in the digital asset ecosystem, the report showcases frequency-severity models based on real loss data for pricing cyber risk in digit assets. The authors also deploy Monte Carlo simulation to estimate the tail risks that reveal practical insights for developing risk management strategies.
Since the use of digital assets will continue to grow, all actuaries will benefit from the education and insight the report provides.
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
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
Authored By Brian Kaul, Janine Bender, ASA, MAAA, Ben Leiser, FSA, MAAA, Lisa Parker, ASA, MAAA, Risk & Regulatory Consulting, LLC
Sponsored by the Joint Risk Management Research Committee
In March of 2020, the global economic order was shaken by the advent of the novel coronavirus pandemic, which prompted widespread government lockdowns, business closures, and stimulus spending. Months into the pandemic, commentators began speaking of a so-called ‘new’ new normal’ as citizens adjusted to the cultural and business changes attendant to mandatory masking, working from home, social distancing, and extensive school closures, along with the widespread rise of DEI departments within corporate and government organizations. In a constantly changing world, the concept of a ‘new’ new normal refers to that which is different from what was experienced in the past, and is now becoming the norm. Going forward, for clarity, this paper will refer to a ‘new normal’ rather than a ‘new’ new normal
Research Briefs
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.
By Aditya Khanna, FCAS; Brian A. Fannin, ACAS, CSPA; and Tim Wei, FCAS
