Overview
- A concise viscosity solution approach in insurance control problems
- Provides existence and structure of optimal strategies
- Offers systematic construction of the optimal value functions
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Quantitative Finance (BRIEFFINANCE)
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Table of contents (6 chapters)
Keywords
About this book
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.
Reviews
“This book mainly contains work done by the authors during the last few years in the area of optimal control of insurance surpluses. … The book is very nicely written and gives an excellent overview of the topic. It is an ideal textbook for all researchers in insurance, in particular for those interested in optimisation problems.” (Hanspeter Schmidli, zbMATH 1308.91004, 2015)
Authors and Affiliations
Bibliographic Information
Book Title: Stochastic Optimization in Insurance
Book Subtitle: A Dynamic Programming Approach
Authors: Pablo Azcue, Nora Muler
Series Title: SpringerBriefs in Quantitative Finance
DOI: https://doi.org/10.1007/978-1-4939-0995-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2014
Softcover ISBN: 978-1-4939-0994-0Published: 20 June 2014
eBook ISBN: 978-1-4939-0995-7Published: 19 June 2014
Series ISSN: 2192-7006
Series E-ISSN: 2192-7014
Edition Number: 1
Number of Pages: X, 146
Number of Illustrations: 17 b/w illustrations, 2 illustrations in colour
Topics: Quantitative Finance, Probability Theory and Stochastic Processes, Insurance