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Aspects of Risk Theory

  • JanĀ Grandell

Part of the Springer Series in Statistics book series (SSS)

Table of contents

  1. Front Matter
    Pages i-x
  2. Jan Grandell
    Pages 1-32
  3. Jan Grandell
    Pages 57-76
  4. Jan Grandell
    Pages 77-124
  5. Jan Grandell
    Pages 125-134
  6. Back Matter
    Pages 135-175

About this book

Introduction

Risk theory, which deals with stochastic models of an insurance business, is a classical application of probability theory. The fundamental problem in risk theory is to investigate the ruin possibility of the risk business. Traditionally the occurrence of the claims is described by a Poisson process and the cost of the claims by a sequence of random variables. This book is a treatise of risk theory with emphasis on models where the occurrence of the claims is described by more general point processes than the Poisson process, such as renewal processes, Cox processes and general stationary point processes. In the Cox case the possibility of risk fluctuation is explicitly taken into account. The presentation is based on modern probabilistic methods rather than on analytic methods. The theory is accompanied with discussions on practical evaluation of ruin probabilities and statistical estimation. Many numerical illustrations of the results are given.

Keywords

Fusion Markov process Martingale Poisson process Random variable Statistica convergence model point process presentation probability probability theory random measure time variable

Authors and affiliations

  • JanĀ Grandell
    • 1
  1. 1.Department of MathematicsThe Royal Institute of TechnologyStockholmSweden

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-9058-9
  • Copyright Information Springer-Verlag New York 1991
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-9060-2
  • Online ISBN 978-1-4613-9058-9
  • Series Print ISSN 0172-7397
  • Buy this book on publisher's site