Pricing Insurance Risk. Stephen J. Mildenhall
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Pricing Insurance Risk
Theory and Practice
Stephen J. Mildenhall and John A. Major
This edition first published 2022
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Library of Congress Cataloging-in-Publication Data Names: Mildenhall, Stephen J., author. | Major, John A., author. Title: Pricing insurance risk : theory and practice / Stephen J Mildenhall, John A Major. Description: Hoboken, NJ : John Wiley and Sons, 2022. | Includes bibliographical references and index. Identifiers: LCCN 2021062792 (print) | LCCN 2021062793 (ebook) | ISBN 9781119755678 (hardback) | ISBN 9781119755692 (pdf) | ISBN 9781119756521 (epub) | ISBN 9781119756538 (ebook) Subjects: LCSH: Risk (Insurance) | Risk management. Classification: LCC HG8054.5 .M55 2022 (print) | LCC HG8054.5 (ebook) | DDC 368–dc23/eng/20220111 LC record available at https://lccn.loc.gov/2021062792 LC ebook record available at https://lccn.loc.gov/2021062793
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Dedicated to our wives, Helen and Diane
Contents
1 Cover
5 Preface
6 1 Introduction1.1 Our Subject and Why It Matters1.2 Players, Roles, and Risk Measures1.3 Book Contents and Structure1.4 What’s in It for the Practitioner?1.5 Where to Start
7 2 The Insurance Market and Our Case Studies2.1 The Insurance Market2.2 Ins Co.: A One-Period Insurer2.3 Model vs. Reality2.4 Examples and Case Studies2.5 Learning Objectives
8 Part I Risk3 Risk and Risk Measures3.1 Risk in Everyday Life3.2 Defining Risk3.3 Taxonomies of Risk3.4 Representing Risk Outcomes3.5 The Lee Diagram and Expected Losses3.6 Risk Measures3.7 Learning Objectives4 Measuring Risk with Quantiles, VaR, and TVaR4.1 Quantiles4.2 Value at Risk4.3 Tail VaR and Related Risk Measures4.4 Differentiating Quantiles, VaR, and TVaR4.5 Learning Objectives5 Properties of Risk Measures and Advanced Topics5.1 Probability Scenarios5.2 Mathematical Properties of Risk Measures5.3 Risk Preferences5.4 The Representation Theorem for Coherent Risk Measures5.5 Delbaen’s Differentiation Theorem5.6 Learning Objectives5.A Lloyd’s Realistic Disaster Scenarios5.B Convergence Assumptions for Random Variables6 Risk Measures in Practice6.1 Selecting a Risk Measure Using the Characterization Method6.2 Risk Measures and Risk Margins6.3 Assessing Tail Risk in a Univariate Distribution6.4 The Intended Purpose: Applications of Risk Measures6.5 Compendium of Risk Measures6.6 Learning Objectives7 Guide to the Practice Chapters
9 Part II Portfolio Pricing8 Classical Portfolio Pricing Theory8.1 Insurance Demand, Supply, and Contracts8.2 Insurer Risk Capital8.3 Accounting Valuation Standards8.4 Actuarial Premium Calculation Principles and Classical Risk Theory8.5 Investment Income