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2703 results in General statistics and probability

Page 42 of 136

  • Preface

  • David Hindley
  • Book:
    Claims Reserving in General Insurance
    Published online:
    27 October 2017
    Print publication:
    26 October 2017, pp ix-x

  • Summary

    Legal disclaimer

    This book is intended to provide information on the subject of claims reserving in general insurance, using descriptive text, worked examples, software code, data and mathematical formulations. The content is intended solely as a learning aid, and should not be used in any particular application without independent testing and verification by the person making the application. In addition, the author and publisher are not offering this book as actuarial, statistical or other professional services advice, and no reliance should be placed on it as such.

    For these reasons, the author and publisher make no warranties, express or implied, that the descriptions, worked examples, software code, data, mathematical formulations, or other information in this volume are free of error, that they are consistent with industry standards, or that they will meet the requirements for any particular application. THE AUTHOR AND PUBLISHER EXPRESSLY DISCLAIM ANY IMPLIEDWARRANTIES OF SATISFACTORY QUALITY MERCHANTABILITY AND OF FITNESS FOR ANY PARTICULAR PURPOSE, even if the author or publisher has been advised of a particular purpose, and even if a particular purpose is indicated in the book. The author and publisher also disclaim all liability for direct, indirect, incidental, or consequential damages that result from any use of the descriptions, worked examples, software code, data, mathematical formulations, or other information in this book.

    Permission to use the third-party content in this volume was obtained for use in this volume only.Neither the publisher nor the author make any representation regarding whether re-use of third-party descriptive text, worked examples, software code, data, mathematical formulation, or other information in this volume might infringe others’ intellectual property rights, including US and foreign patents. It is the reader's sole responsibility to ensure that he or she is not infringing any third-party intellectual property rights, even for use which is considered to be experimental in nature. By using any of the third-party descriptive text, worked examples, software code, data, mathematical formulations or other information in this volume, the reader has agreed to assume all liability for any damages arising from or relating to such use, regardless of whether such liability is based on intellectual property or any other cause of action, and regardless of whether the damages are direct, indirect, incidental, consequential, or any other type of damage. The authors and publisher disclaim any such liability for re-use of third-party content.

  • 3 - Deterministic Reserving Methods

  • David Hindley
  • Book:
    Claims Reserving in General Insurance
    Published online:
    27 October 2017
    Print publication:
    26 October 2017, pp 40-145

  • Summary

    Introduction

    This chapter describes several of the reserving methods that can be used to derive reserve estimates. The methods are labelled as “deterministic”, to distinguish them from stochastic methods, which are described in Chapter 4. The termdeterministic in this context is intended to mean that the method will typically produce a single or “point” estimate of the reserves, without an assessment of the statistical variability around that estimate. Such methods can, however, be used to provide a range of results by varying the assumptions used within the method.

    Although deterministic methods are different in nature to stochastic methods, they are still sometimes referred to as “statistical” methods, to distinguish them from case by case type approaches, in which the reserves are determined by merely adding up all the individual case reserves for each reported claim. The use of the term statistical in this way is not intended to mean that the methods are based on a formal statistical model.

    In practice, deterministic methods are used in most cases where a single point estimate of reserves is required, notwithstanding the fact that stochastic methods can also be used to produce a point estimate. For both types of method, they will usually be applied within the context of an overall reserving process, as opposed to a confined theoretical context. This process is outlined in Chapter 1. Although this chapter focuses on explaining the methods themselves, it does also include some high-level comments relating to their practical application, with additional details being given in Chapters 5, 6 and 7.

    The goal of applying the reserving methods described in this chapter is assumed to be to estimate the ultimate claims and hence the corresponding Claims Reserve (as defined in Chapter 1) – that is the total amount relating to Case Reserves, IBNR and IBNER. Different methods are usually needed to derive the other types of reserve described in that chapter, such as ULAE and UPR. Where relevant, reference is made to the methods that can be used for these other reserve types in Chapter 6.

    These methods are assumed to be applied to data organised in a triangle format (which was introduced in Chapter 2), and to one triangle at a time, unless stated otherwise.

  • 5 - Reserving in Practice

  • David Hindley
  • Book:
    Claims Reserving in General Insurance
    Published online:
    27 October 2017
    Print publication:
    26 October 2017, pp 320-345

  • Summary

    Introduction

    The main purpose of this chapter is to summarise a number of key generic aspects of reserving in practice. It is designed mainly for the practitioner who is new or relatively new to reserving, although some of the content may also be helpful to more experienced practitioners when they are reviewing their overall reserving process.

    This chapter builds on the various other practical aspects of reserving covered in other chapters. For example, some of the practical details of applying specific reserving methods are covered in Chapters 3 and 4 for deterministic and stochastic methods respectively. Chapter 6 also covers a number of reserving topics that may be relevant to applying methods in practice, such as the use of Actual vs Expected methodology and discounting.

    Inevitably, in any reserving exercise there will be points of detail that depend, for example, on the nature of the business being analysed and the purpose of the exercise. Chapter 7 summarises some of this detail for a selected range of specific contexts, such as UK Motor and US Workers’ Compensation.

    Hence, many of the chapters have material which is relevant to reserving in practice. Together, this content refers to the “art” of reserving, to supplement the other parts of the book, which focus more on the “science” of reserving; reserving work in practice will typically involve both of these aspects.

    In Chapter 1, a reserving exercise was summarised as having four key stages – Background, Data, Analysis and Reporting–with brief details being provided on each of these stages. The current chapter provides some additional practical details of selected aspects of each of these stages. The first two stages – Background and Data – have already been covered in earlier chapters in sufficient detail, so this chapter only includes relevant additional points, to help put these stages in the context of the overall reserving process. The Analysis stage is covered in several sections, relating to various aspects of this stage of the process, which forms the core of most reserving exercises.

    The focus in this chapter is on using deterministic methods to derive a point estimate of the reserves, for example, for financial reporting purposes.

  • 7 - Reserving in Specific Contexts

  • David Hindley
  • Book:
    Claims Reserving in General Insurance
    Published online:
    27 October 2017
    Print publication:
    26 October 2017, pp 410-464

  • Summary

    Introduction

    This chapter provides details of selected key features of reserving in a range of specific contexts. For each territory/class considered, matters such as a description of the class, data types and example reserving methods are given. The drafting of this chapter has taken into account input from individuals or firms who have particular knowledge and experience in each of the relevant areas, as noted in the acknowledgements in Section 1.6. The generic matters that are relevant to all reserving exercises, such as understanding the business, checking the data and using homogeneous data groupings, are not repeated here, as they are already covered in the earlier chapters. Similarly, the generic points related to the application of individual reserving methods are also not repeated here, as they are covered in the description of each method in the relevant chapters.

    The purpose of collating these details is to give some preliminary information in relation to reserving in the relevant contexts. For each context, it is assumed that themain purpose of the reserving exercise is to determine a point estimate of the reserves for financial reporting purposes. Partly as a consequence of this, the reserving methods referred to are mostly deterministic in nature. In practice, stochastic methods are also likely to be used for some purposes in a number of the different contexts. Where more than one reserving method is mentioned, it is common in most contexts for the final selected results to be based on a combination of different methods, which may vary across the cohorts, as explained in general terms in Section 5.7.

    This chapter is not intended to be an instruction manual for the application of the reserving methods described in the earlier chapters, and does not represent any form of recommended approach, guidance or actuarial/professional standard. In practice, for each territory/class there will be many variations and additional detail beyond that described here, which in most cases will be learned through several years of practical experience. Furthermore, in some cases, the application of reserving methods will differ from that described here, perhaps significantly so, due to the specific circumstances.

    The various subdivisions of data given for each territory/class are not mutually exclusive and combinations of them may often be used in practice.

  • 1 - Introduction

  • David Hindley
  • Book:
    Claims Reserving in General Insurance
    Published online:
    27 October 2017
    Print publication:
    26 October 2017, pp 1-15

  • Summary

    The process of claims reserving is at the core of the financial management of general insurance organisations. It determines what is held on the balance sheet for claims that are not yet settled, affects the premiums that are charged and impacts on the capital that is held to support the solvency of the organisation. Thus, the selection of appropriate reserving methodologies and assumptions, and the application to practical situations, often with imperfect data, are of critical importance to the operations of an insurance organisation. This book has been designed for both those who are relatively newto the subject of reserving in general insurance, and for experienced practitioners who want a single reference source on the subject. It is also anticipated that it will be of interest to those wanting to develop new reserving techniques.

  • To produce a comprehensive description of both the theory and practice of claims reserving in general insurance. Although there are already a large number of papers and books on this subject, I have always felt that creating a single reference work covering a wide range of reserving topics would be of benefit to those new to the subject and to experienced practitioners, partly to help avoid the reinvention of previously developed approaches that I have seen occur several times during my career (by others and myself). Although most reserving is nowcarried out in bespoke or proprietary reserving software, which will usually have associated user guides and manuals, this book is intended to supplement those sources by covering a variety of reserving topics and techniques, the latter of which may not all be implemented in the relevant software products.

  • To provide those who wish to advance the more theoretical aspects of reserving with a clear and thorough description of the many practical issues that frequently occur when applying reserving methods in the real world. My hope is that, by doing this, more effective new approaches can be developed in future which make appropriate allowance for these practical issues, which in turn should encourage their wider application. In so doing, this should improve the reliability of reserve estimates and assist with understanding the uncertainty surrounding those estimates.More accurate reserve estimates should lead to fairer insurance/reinsurance premiums and to more reliable financial statements, both of which must be in the public interest.

Page 42 of 136