Pricing Insurance Risk. Stephen J. Mildenhall

      

Pricing Insurance Risk

      Theory and Practice

       Stephen J. Mildenhall and John A. Major

This edition first published 2022

      © 2022 John Wiley & Sons, Inc.

      All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

      The right of Stephen J. Mildenhall and John A. Major to be identified as the authors of this work has been asserted in accordance with law.

       Registered Office

      John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA

       Editorial Office

      111 River Street, Hoboken, NJ 07030, USA

      For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com.

      Wiley also publishes its books in a variety of electronic formats and by print-on-demand. Some content that appears in standard print versions of this book may not be available in other formats.

       Limit of Liability/Disclaimer ofWarranty

      While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

      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

      Cover Design: Wiley

      Cover Image: © zef art/Shutterstock

      Set in 9.5/12.5pt STIXTwoText by Integra Software Services Pvt. Ltd, Pondicherry, India

Dedicated to our wives, Helen and Diane

Contents

      1  Cover

      2  Title page

      3  Copyright

      4  Dedication

      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 in Pricing8.6 Financial Valuation and Perfect Market Models8.7 The Discounted Cash Flow Model8.8 Insurance Option Pricing Models8.9 Insurance Market Imperfections8.10 Learning Objectives8.A Short- and Long-Duration Contracts8.B The Equivalence Principle9 Classical Portfolio Pricing Practice9.1 Stand-Alone Classical PCPs9.2 Portfolio CCoC Pricing9.3 Applications of Classical Risk Theory9.4 Option Pricing Examples9.5 Learning Objectives10 Modern