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2000 | Buch

Loss Reserving

An Actuarial Perspective

verfasst von: Greg Taylor

Verlag: Springer US

Buchreihe : Catastrophe Modeling

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Über dieses Buch

All property and casualty insurers are required to carry out loss reserving as a statutory accounting function. Thus, loss reserving is an essential sphere of activity, and one with its own specialized body of knowledge. While few books have been devoted to the topic, the amount of published research literature on loss reserving has almost doubled in size during the last fifteen years.
Greg Taylor's book aims to provide a comprehensive, state-of-the-art treatment of loss reserving that reflects contemporary research advances to date. Divided into two parts, the book covers both the conventional techniques widely used in practice, and more specialized loss reserving techniques employing stochastic models. Part I, Deterministic Models, covers very practical issues through the abundant use of numerical examples that fully develop the techniques under consideration. Part II, Stochastic Models, begins with a chapter that sets up the additional theoretical material needed to illustrate stochastic modeling. The remaining chapters in Part II are self-contained, and thus can be approached independently of each other. A special feature of the book is the use throughout of a single real life data set to illustrate the numerical examples and new techniques presented. The data set illustrates most of the difficult situations presented in actuarial practice. This book will meet the needs for a reference work as well as for a textbook on loss reserving.

Inhaltsverzeichnis

Frontmatter

Deterministic Models

Frontmatter
1. Basic Concepts
Abstract
First, some basic terminology. This volume will be concerned with the branch of insurance known variously as:
  • property and casualty insurance (United States)
  • non-life insurance (Continental Europe)
  • general insurance (Great Britain).
Greg Taylor
2. Claim Counts
Abstract
This chapter will be directed towards the estimation of IBNR claims counts. In this context, only the interpretation of period of origin as period of occurrence is relevant.
Greg Taylor
3. Claim Amounts - Simple Models
Abstract
A case estimate is an estimate of outstanding losses in respect of an individual claim. It may also be referred to as:
  • • an individual estimate
  • • a manual estimate
  • • a physical estimate.
Greg Taylor
4. Claim Amounts - Other Deterministic Models
Abstract
This chapter will make an attempt to remedy the very empirical nature of the chain ladder and separation methods on which comment has been made in Sections 3.2.4 and 3.3.4. This will be done by examining the mechanics of the claim process in a little greater detail.
Greg Taylor
5. Combination of Deterministic Estimates of Liability
Abstract
and have discussed and illustrated a number of different models for the estimation of outstanding claims liability. Table 5.1 summarises the numerical results obtained.
Greg Taylor

Stochastic Models

Frontmatter
6. Stochastic Techniques
Abstract
Subsequent chapters examine various stochastic models of the claims process. The present chapter provides some theoretical foundation for this.
Greg Taylor
7. Stochastic Chain Ladder
Abstract
The chain ladder was introduced in Chapter 2, where three different derivations were given. Two of these, Derivations 2 and 3, had stochastic bases. For example, Derivation 2 involves a fully parametric model.
Greg Taylor
8. Stochastic Models with a GLM Basis
Abstract
was concerned with the chain ladder in a stochastic setting. The log-linearity ofthat model was pointed out in Section 7.2.
Greg Taylor
9. Credibility Models
Abstract
The credibility model (6.21) may be adapted to the context of loss statistics as follows:
$$E[Y\mathop {(i,j)}\limits_{1 \times 1} \left| {\theta (i,j)} \right.] = X\mathop {(i,j)}\limits_{1 \times p} \beta \mathop {[\theta (i,j)]}\limits_{p \times 1} ,$$
(9.1)
where Y is some array of loss statistics indexed in the usual way by period of origin i and development period j.
Greg Taylor
10. Kalman Filter
Abstract
Consider again the example dealt with in Section 9.3.3. Its defining property was that each period of origin i was characterised by a parameter vector β [θ (i)], which was allowed to vary with i.
Greg Taylor
11. Bootstrap
Abstract
The bootstrap was described in general terms in Section 6.5. The present chapter illustrates its use by application of it to the stochastic chain ladder model dealt with in Section 7.3. The illustration will follow the framework set out in Section 6.5, with particular emphasis on matters of practical detail.
Greg Taylor
12. Final Estimates of Liability
Abstract
Chapter 3 and Chapter 4 introduced a range of deterministic models and Chapter 7 to 10 a range of stochastic models and introduced a range of deterministic models and to a range of stochastic models. After the application of some or all of these to a data set, the actuary will need to choose final estimates of the liability for outstanding losses.
Greg Taylor
Backmatter
Metadaten
Titel
Loss Reserving
verfasst von
Greg Taylor
Copyright-Jahr
2000
Verlag
Springer US
Electronic ISBN
978-1-4615-4583-5
Print ISBN
978-1-4613-7070-3
DOI
https://doi.org/10.1007/978-1-4615-4583-5