The book develops the capabilities arising from the cooperation between mathematicians and statisticians working in insurance and finance fields. It gathers some of the papers presented at the conference MAF2010, held in Ravello (Amalfi coast), and successively, after a reviewing process, worked out to this aim.

to Actuarial Mathematics by A. K. Gupta Bowling Green State University, Bowling Green, Ohio, U. S. A. and T. Varga National Pension Insurance Fund. Budapest, Hungary SPRINGER-SCIENCE+BUSINESS MEDIA, B. V. A C. I. P. Catalogue record for this book is available from the Library of Congress. ISBN 978-90-481-5949-9 ISBN 978-94-017-0711-4 (eBook) DOI 10. 1007/978-94-017-0711-4 Printed on acid-free paper All Rights Reserved (c) 2002 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2002 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. To Alka, Mita, and Nisha AKG To Terezia and Julianna TV TABLE OF CONTENTS PREFACE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix CHAPTER 1. FINANCIAL MATHEMATICS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1. Compound Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2. Present Value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1. 3. Annuities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 CHAPTER 2. MORTALITy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2. 1 Survival Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2. 2. Actuarial Functions of Mortality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 2. 3. Mortality Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 CHAPTER 3. LIFE INSURANCES AND ANNUITIES . . . . . . . . . . . . . . . . . . . . . 112 3. 1. Stochastic Cash Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 3. 2. Pure Endowments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 3. 3. Life Insurances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 3. 4. Endowments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 3. 5. Life Annuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 CHAPTER 4. PREMIUMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 4. 1. Net Premiums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 4. 2. Gross Premiums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Vll CHAPTER 5. RESERVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 5. 1. Net Premium Reserves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 5. 2. Mortality Profit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 5. 3. Modified Reserves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 ANSWERS TO ODD-NuMBERED PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Consumer Attitudes Toward Credit Insurance provides the findings of a survey of approximately 3600 individuals who had the opportunity to purchase credit life insurance in conjunction with all types of consumer loans, except first mortgages and credit cards. The survey that forms the basis of the book was conducted in 1993 by the Credit Research Center at Purdue University's Krannert Graduate School of Management. It replicates and expands upon four previous national studies of credit insurance consumers, done between 1970 and 1985. Despite the generally positive findings of prior research with respect to consumer attitudes toward credit insurance, several open questions remain of interest to policy makers, specifically the question of whether coercion is involved in the sale of the insurance. Consumer Attitudes Toward Credit Insurance addresses these outstanding issues. It presents a profile of who is currently being served by the credit insurance market, as well as the reasons borrowers purchase the product and their experience with the offer of credit insurance at point of sale.

This book expertly introduces and clearly explains all topics covered in marine insurance law courses at undergraduate and postgraduate levels, offering students and those new to the area a comprehensive and accessible overview of this important topic in commercial law. Beginning by introducing the general principles of the subject, the structure and formation of insurance contracts, Marine Insurance Law then looks to individual considerations in detail, including: brokers, losses, risks and perils, sue and labour, reinsurance, and mutual insurance/P&I clubs. This title has been developed with the needs of courses specifically in mind, and its content has been tailored to include the most important and commonly taught topics in the field. Each chapter contains end of chapter further reading to support student research, ensuring this new textbook provides a reliable and accessible gateway into this important topic in maritime law

Introduction This book includes terms of reference and offers an augmented volume of relevant work initiated within the comprehensive concept of "Knowledge Management and Risk Governance." The latter stood for the initial title of an ad-hoc meeting held in Ascona, Switzerland, organized by the Technological Risk Management Unit of the Joint Research Centre of the European Commission (JRC) and the KOVERS Centre of Excellence in Risk and Safety Sciences of the Swiss Federal Institute of Technology, ETH Zurich. Background Risk governance, in addition to the continuous interest of researchers, has recently attracted the attention of policy-makers and the media and the concern of the public. New and emerging risks in various fields and a number of risk-related issues increased the public interest and prompted for a new framework in dealing with risks. The Conference on Science and Governance organized by the European Commission in October 2000 is one of the international forums addressing this issue. Other recent events such as the establishment of the International Risk Governance Council outline the importance of the governance concept in relation to that of risk management (see www.irgc.org). At the same time noticeable progress has been made in Information Technologies and Decision Support, passing from the process of information PREFACE xvi to the process of knowledge. In this context new tools and methods became available, whose application in risk management may be beneficial.

An Introduction to Actuarial Studies provides a contemporary guide to actuarial technique and practice. This substantially revised and extended new edition includes: New and thoroughly updated material Many more exercises with solutions to allow the reader to establish confidence in using actuarial techniques. It covers a broad range of topics representing the basic areas of actuarial science including compound interest calculations, demographic theory and techniques, and the pricing and operation of simple life assurance contracts. Numerous worked examples illustrate the principles and techniques described in the text. The text assumes no prior knowledge of actuarial work but requires mathematical knowledge at first year university level and an ability for problem solving. It is designed both for those beginning a career in actuarial work, as well as those interested in learning about basic actuarial tools and the main areas of actuarial practice. Contents: Preface; 1. Introduction; 2. Valuation of Financial Transactions; 3. Demography; 4. Actuarial Practice; 5. Valuation of Contingent Payments; References; Index

This book explores the ways in which the adoption of new paradigms, processes, and technologies can lead to greater revenue, cost efficiency and control, as well as improved business agility in the insurance industry.

One measure of public program response to rapidly expanding older populations is the approach to old-age pensions under social insurance, social assistance, and provident fund systems. Social insurance is clearly the preferred method of meeting the income needs of the elderly, but historical, as well as current social and economic conditions are forcing many nations to reevaluate the characteristics of viable and sustainable social insurance programs. This has led to a variety of innovations in old-age pension programs development, including revised benefit formulas, raised retirement ages, increased income testing, and expanded reliance on private occupational supplemental programs.

The essays in this new international handbook analyze the impact of the economic, social, and cultural effects of aging populations on government social insurance policies. They offer a perspective on how twenty different countries have approached income maintenance programs for the elderly. Collectively, the contributors demonstrate how governments, non-governmental entities, communities, and families respond to changes in traditional income and social service support systems. They provide not only descriptions of existing programs, but also a better understanding of the factors that gave rise to their distinct characteristics. This important new collection will be required reading for everyone involved in elderly services.

The articles in this volume were first presented at the Seventh and Eighth Conferences on Economic Issues in Workers' Compensation sponsored by the National Council on Compensation Insurance. A principal objective of the Conference series has been for workers' compensation insurance researchers to apply state-of-the-art research methodologies to policy questions of interest to the workers' compensation insurance community. This community is a rather diverse group--it includes employers, insurers, injured workers, regulators, and legislators, as well as those who service or represent these groups (e.g., physicians, rehabilitation specialists, labor unions). Despite this diversity and the variety of agendas, the Conference series continues to address many important policy questions. Readers familiar with the Conference series and the four previously published volumes should notice an evolution in terms of the topics addressed in this volume. In the earlier conferences, the topics were more often concerned with the underlying causes of the tremendous increase in workers' compensation benefit payments. In the present volume, h- ever, only four of the fourteen chapters directly concern workers' c- pensation insurance benefits, while the other ten concern the pricing of workers compensation insurance. This is not to suggest that workers' compensation cost increases have abated. In 1989, workers' compensation incurred losses exceeded $45 billion to continue the annual double-digit cost increases. Two explanations can be offered for the somewhat altered focus of this volume. First, despite the continued increase in prices, the financial results for the workers' compensation insurance line continue to be poor.

This book explores the central problems underlying the insurance of aviation war and terrorism risks and associated perils. It critically analyses the reasons why conventional insurance markets are unwilling or unable to provide sustainable insurance coverage for aviation war and terrorism risks in the aftermath of catastrophic events such as the terrorist events of September 11, 2001. It also examines some of the prominent concepts proposed and/or implemented after 9/11 to determine whether and to what extent these concepts avoid identified pitfalls. Like many of life s essentials, the importance of insurance is most evident when it is not available. The sheer scale and magnitude of the insurance losses that followed 9/11 caused conventional insurance markets (which hitherto had been offering generous insurance coverage for aviation war and terrorism risks to air transport operators for little or no premium) to withdraw coverage forthwith. The ensuing absence or insufficiency of commercial insurance coverage for aviation war and terrorism risks has sparked a global search for viable and sustainable alternatives. Ten years have since elapsed, and despite numerous efforts, the fundamental problems remain unresolved. The book proceeds on the premise that the underlying issues are not entirely legal in nature; they have immense economic, psychological and policy implications that cannot be underestimated. A multidisciplinary approach is therefore used in examining the issues, drawing heavily upon analytical principles adapted from law and economics and behavioural law and economics. It is hoped that the resulting study will be beneficial not only to lawyers and those interested in aviation insurance but also to economists, air transport insurance program managers, capital market investors and governmental policymakers, both at the national and international levels.

Employers Can Reduce Their Employees' Health Care Costs by Thinking Out of The BoxEmployee health care costs have skyrocketed, especially for small business owners. But employers have options that medical entrepreneurs have crafted to provide all businesses with plans to improve their employees' wellness and reduce their costs. Thus, the cost of employee health care benefits can be reduced markedly by choosing one of numerous alternatives to traditional indemnity policies. The Finance of Health Care provides business decision makers with the information they need to match the optimal health care plan with the culture of their workforce. This book is a must guide for corporate executives and entrepreneurs who want to attract-and keep--the best employees in our competitive economy.

The problem of solvency is, in fact, as old as insurance. The history of the industry knows many ways to meet the risks involved with underwriting, such as spreading the risk portfolio (Cato, Senior already applied it), risk selection, reserve funds, reinsurance, etc. Whilst these measures too often proved ineffective, the establish ment of legislative control and public supervision ensued. However, not until the last few decades has the solvency issue become an ob ject of intensive studies, very much thanks to the progress of related empirical and theoretical knowledge, and in the under standing of the concerned complicated processes. The research activities have grown extensively in many countries in recent years. The more the studies advance the more new relevant aspects are detected and a great variety of alternative proposals have come up for discussion. Therefore, it has become necessary to attempt a survey of the whole problem area in order to be able to place the quite numerous pieces of knowledge in their proper context, and also, among other things, to avoid the pitfalls of handling isolated problems omitting vital tie-ins to the environment. Many of the rele vant problems and subproblems are still lacking adequate and well tested solutions. Therefore, a survey of the whole problem area can also hopefully serve as guidance for future research efforts."

The increasingly risky environment in which companies operate is characterized by a rising number of risk components, factors, sources, and drivers. The identification, evaluation, and management of these risks require the capability to coordinate various skills within a company and in upstream and downstream relationships. This handbook provides an integrated approach to the assessment, transfer, and communication of critical risks and highlights emerging methodologies that can help to protect businesses from adverse events and their effects. It explains how different risk management perspectives should be combined, and in particular how the corporate governance vision should be integrated with the perspectives of operations management, financial management, and business continuity management. In this sense the handbook provides concrete directions on how to develop a risk management team and culture, taking into account business challenges and employing appropriate managerial tools.

Using institutional theory to explain innovation and merging academic and critical analysis with practical recommendations, this book provides a full and rich account of how new products are brought to market; considering both the successes and failures in equal measure. This book takes the meeting point of two seemingly incongruous schools of theoretical thought to enlighten the debate surrounding product innovation. In doing so it: illustrates how institutional forces come to shape the interest, priorities and behaviour of organizational members in the development and implementation process of incremental product innovation investigates the failed innovative attempts of established organizations demonstrates the importance of organizational and intra-organizational forces for innovative success. The insight it offers into the organization of product innovation processes in the financial services sector and the guidelines it sets up for their improvement makes Innovation and Institutions essential reading for those working in or studying the banking, finance and insurance sector who have an interest in innovation studies.

Poor health habits (drinking, smoking, lack of exercise) obviously take their toll on individuals and their families. The costs to society are less obvious but certainly more far-reaching. This investigation is the first to quantify the financial burden these detrimental habits place on American taxpayers. Willard Manning and his colleagues measure the direct costs of poor health habits (fire damage, motor vehicle accidents, legal fees), as well as collectively financed costs (medical care, employee sick leave, group health and life insurance, nursing home care, retirement pensions, liability insurance). Consider two co-workers covered by their employer's health plan: both pay the same premium, yet if one drinks heavily, the other--through their mutual insurance program--involuntarily funds the resulting health problems.

After laying out their conceptual framework, methods, and analytical approach, the authors describe precisely how and to what extent drinking, smoking, and lack of exercise are currently subsidized, and make recommendations for reducing or reallocating the expense. They present, for example, a persuasive case for raising excise taxes on alcohol. The authors correlate their data to make costs comparable, to avoid double counting, and to determine the exact costs of each of these poor health habits and some of their findings are quite surprising.

This unique study will be indispensable to public health policy specialists and researchers, as well as to health economists.

Loss Prevention and Security Procedures assists CEOs, security management and loss prevention specialists in dealing with loss. Losses in an organization may originate from a variety of threats, including natural disasters such as earthquakes, tornadoes, and flooding. However, many of the threats to our assets are posed by individuals and may include drug activity, violence, theft and fraud. Loss Prevention and Security Procedures deals specifically with these and many more problems facing today' s security conscious professional.

Written from the management perspective, Loss Prevention and Security Procedures offers discernment and wisdom directed toward the philosophy of anticipatory security, before losses occur and resolving them through the most cost effective initiatives possible.
Serves security professionals in a hands-on, practical manner
Appeals to a mixed audience - it addresses the subject for the benefit of executive management as well as security practitioners
Includes practical forms

The mathematical theory of non-life insurance developed much later than the theory of life insurance. The problems that occur in the former field are far more intricate for several reasons: 1. In the field oflife insurance, the company usually has to pay a claim on the policy only once: the insured dies or the policy matures only once. It is with only a few particular types of policy (for instance, sickness insurance, when the insured starts working again after a period of sickness) that a valid claim can be made on a number of different occasions. On the other hand, the general rule in non-life insurance is that the policyholder is liable to be the victim of several losses (in automobile insurance, of course, but also in burglary and fire insurance, householders' comprehensive insurance, and so on). 2. In the field of life insurance, the amount to be paid by the company excluding any bonuses-is determined at the inception of the policy. For the various types of life insurance contracts, the sum payable on death or at maturity of the policy is known in advance. In the field of non-life insurance, the amount of a loss is a random variable: the cost of an automobile crash, the partial or totalloss of a building as a result of fire, the number and nature of injuries, and so forth."

This book addresses an experiment in funding money damage claims in England from 2000 to 2013. The model - recoverable conditional fees - was unique and has remained so. It covers the development, amendment and effective abolition of the model, as well as the process of policy development and the motivation and objectives of the policy makers.