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

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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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.

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