Stochastic Optimization in Insurance

A Dynamic Programming Approach

  • Pablo Azcue
  • Nora Muler

Part of the SpringerBriefs in Quantitative Finance book series (BRIEFFINANCE)

Table of contents

  1. Front Matter
    Pages i-x
  2. Pablo Azcue, Nora Muler
    Pages 1-21
  3. Pablo Azcue, Nora Muler
    Pages 23-49
  4. Pablo Azcue, Nora Muler
    Pages 51-73
  5. Pablo Azcue, Nora Muler
    Pages 75-96
  6. Pablo Azcue, Nora Muler
    Pages 97-122
  7. Pablo Azcue, Nora Muler
    Pages 123-134
  8. Back Matter
    Pages 135-146

About this book

Introduction

The main purpose of the book is to show how a viscosity approach can be used to tackle control problems in insurance. The problems covered are the maximization of survival probability as well as the maximization of dividends in the classical collective risk model. The authors consider the possibility of controlling the risk process by reinsurance as well as by investments. They show that optimal value functions are characterized as either the unique or the smallest viscosity solution of the associated Hamilton-Jacobi-Bellman equation; they also study the structure of the optimal strategies and show how to find them.

The viscosity approach was widely used in control problems related to mathematical finance but until quite recently it was not used to solve control problems related to actuarial mathematical science. This book is designed to familiarize the reader on how to use this approach. The intended audience is graduate students as well as researchers in this area.

Keywords

Band strategies Classical collective risk model Dynamic programming principle HJB equation Ruin probability Viscosity solutions

Authors and affiliations

  • Pablo Azcue
    • 1
  • Nora Muler
    • 2
  1. 1.Dpt of Mathematics & StatisticsUniversidad Torcuato Di TellaBuenos AiresArgentina
  2. 2.Dpt of Mathematics & StatisticsUniversidad Torcuato Di TellaBuenos AiresArgentina

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-0995-7
  • Copyright Information The Author(s) 2014
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-0994-0
  • Online ISBN 978-1-4939-0995-7
  • Series Print ISSN 2192-7006
  • Series Online ISSN 2192-7014
  • About this book
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