Stephen J. Mildenhall - Pricing Insurance Risk

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Pricing Insurance Risk is a topic of great concern to actuaries, especially property-casualty actuaries, our primary audience. But it is also relevant to those working in other fields, including risk management and Enterprise Risk Management, capital modeling, catastrophe modeling, financial regulation, and solvency assessment. Insurance risk is managed through pooling, unlike financial risk that is managed through hedging. The title could have been Pricing Non-Hedgeable Risk.

The book came about through a confluence of supporting factors. We had worked independently for many years on the problem of defining the value of risk management and risk transfer (especially in the context of property catastrophe risk) and “escaping the efficient frontier.” Don Mango brought us together to work with him and Jesse Nickerson to present a multipart tutorial on spectral risk measures at the Casualty Actuarial Society Spring 2018 meeting. The tutorial was so successful that we felt it deserved a wider audience and set about developing a monograph: “Spectral Risk Measures for the Working Actuary.” As we proceeded to refine our thinking and presentation, we realized there was so much more to be explained. Three and a half years and 1200 git commits later, we had this book.

The literature is rich with good answers to many fundamental questions about insurance risk that are consistent with finance theory and relatively easy to apply. Much is known, in the sense of being out there in the literature, but too much is not widely known by people who would benefit from that knowledge. Actuarial education and practice in this area lags the state of the art. We have encountered actuaries struggling with ill-defined terminology and concepts with multiple names. We have seen confusion wrought by inappropriate application of finance theories (remember the underwriting beta?). Our newly minted US Fellows are often ignorant of the latest developments because they are not on the exam syllabus and there has not been an easy way to incorporate them.

This book presents these good answers in one systematic and comprehensive source for the first time, making them much more accessible to actuaries and other practitioners. With this book we intend to raise the bar in actuarial education, enable clear communications, and improve the efficiency of actuaries everywhere by delivering a fresh map of the conceptual territory. We wish we could take credit for the theory we present, but most of it is around twenty years old. We are simply reporting the work of others.

Insurance pricing is multidisciplinary, combining actuarial science and risk theory, probability and statistics, finance and economics, accounting and law. As we organized and synthesized a body of literature as nearly as old as the industry itself to tell the story of insurance pricing, we tried to be sensitive to its historical development—a play some of which we watched unfold in real time. It is a story we both found fascinating. From defining underwriting profit and a reasonable target profit in the 1920s to arguments about investment income in the 1960s. From systematic risk and option pricing theory applications in the 1980s to a more insurance-specific model in the 1990s. And most recently to the introduction of coherent, convex, and even star-shaped risk measures. We hope the reader has time to appreciate the giants on whose shoulders we are lucky enough to stand and can join us in taking in the spectacular vistas of the meaning, quantification, and management of risk they have revealed.

In putting together this book we tried to stay reasonably rigorous without getting lost in a theorem-proof wilderness. We feel strongly that knowing how to use a technique is not helpful if you are unsure that it is valid to use in the first place! We include technical remarks and provide pointers into the literature (about 300 bibliographic references) for those who want a more thorough understanding of “why.” For the practitioner, we included nearly 100 examples and 150 exercises. The Learning Objectives at the end of each chapter summarize what we hope the reader will take away from it. Boldwords and phrases introduce terminology that is used throughout the book.

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