Stochastic Optimization in Insurance
A Dynamic Programming Approach
1st Edition
Published on 19. June 2014
X, 146 pages
978-1-4939-0995-7 (ISBN)
Description
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 / Votes
"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)
More details
Series
Language
English
Place of publication
New York
United States
Publishing group
Springer US
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
X, 146 p. 19 illus., 2 illus. in color.
File size
2,38 MB
ISBN-13
978-1-4939-0995-7 (9781493909957)
DOI
10.1007/978-1-4939-0995-7
Schweitzer Classification
Other editions
Additional editions
Book
06/2014
Springer
€53.49
Shipment within 15-20 days
Content
Stability Criteria for Insurance Companies.- Reinsurance and Investment.- Viscosity Solutions.- Characterization of Value Functions.- Optimal Strategies.- Numerical Examples.- References.- Appendix A. Probability Theory and Stochastic Processes.- Index.
