Reinsurance

Actuarial and Statistical Aspects

Hansjörg Albrecher, Jan Beirlant, Jozef L. Teugels

• Publisher: Wiley
• Year: 2017
• Print ISBN: 9780470772683
• eBook ISBN: 9781119419945
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Reinsurance: Actuarial and Statistical Aspects provides a survey of both the academic literature in the field as well as challenges appearing in reinsurance practice and puts the two in perspective. The book is written for researchers with an interest in reinsurance problems, for graduate students with a basic knowledge of probability and statistics as well as for reinsurance practitioners. The focus of the book is on modelling together with the statistical challenges that go along with it. The discussed statistical approaches are illustrated alongside six case studies of insurance loss data sets, ranging from MTPL over fire to storm and flood loss data. Some of the presented material also contains new results that have not yet been published in the research literature. An extensive bibliography provides readers with links for further study.

1
Introduction

1.1 What is Reinsurance?

A reinsurance contract is an agreement in which one party (the reinsurer) agrees to indemnify another party (the reinsured, the first‐line insurer or also the ceding company, cedent) for specified parts of its underwritten insurance risk. In turn, the cedent pays to the reinsurer a reinsurance premium for this service. That is, in reinsurance the principle of insurance is lifted up one level, so an insurance company seeks itself the possibility of replacing parts of its future loss by a fixed premium payment (much like a policyholder does when entering an insurance contract). There are many reasons why such a risk transfer from the insurer to the reinsurer can be desirable for both parties, as well as for the economy in general, and we will outline a number of them in Section 1.2.

While reinsurance can be seen as a particular form of insurance, and naturally shares various common features with it, reinsurance is also quite distinct from primary insurance in a number of aspects. These include the type and magnitude of risks under consideration, the type of data available for the risk analysis, the diversification possibilities, demand/supply peculiarities of contracts quite different from the primary insurance market, and also the fact that reinsurance is a form of risk sharing among two “professional” insurance entities, so that the necessary guidelines for regulation can be quite different.

(Non‐life) reinsurance contracts are typically written for one year, and one distinguishes between obligatory treaties, where a binding agreement is specified that applies to all risks of a specified risk class, and facultative arrangements, which are negotiated on each individual risk. A facultative treaty is then a contract where the cedent has the option to cede and the reinsurer has the option to decline or accept classified risks of a particular business line. In practice many contracts actually involve several reinsurers (e.g., the contract is negotiated with a primary reinsurer, and other reinsurers then participate proportionally in the reinsurance coverage, or a second reinsurance contract with another reinsurer is written for parts of the remaining risk of the cedent after a first contract). The relationship between insurer and reinsurer is often of a long‐term nature, which also has an effect on the way reinsurance premiums are negotiated. Finally, there is no relation between a reinsurer and the individual policyholders of the underlying risks. A reinsurer may itself enter a reinsurance contract with another insurance company on parts of the reinsured risk, and such a procedure is called retrocession.

Table 1.1 gives a feeling...

Table of contents

• Cover
• Title Page
• Table of Contents
• Preface
• 1 Introduction
• 2 Reinsurance Forms and their Properties
• 3 Models for Claim Sizes
• 4 Statistics for Claim Sizes
• 5 Models for Claim Counts
• 6 Total Claim Amount
• 7 Reinsurance Pricing
• 8 Choice of Reinsurance
• 9 Simulation
• 10 Further Topics
• References
• Index
• End User License Agreement