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Stochastic optimization in insurance : a dynamic programming approach

Author: Pablo Azcue; Nora Muler
Publisher: New York, NY : Springer, 2014.
Series: SpringerBriefs in quantitative finance
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Pablo Azcue; Nora Muler
ISBN: 9781493909957 1493909959 1493909940 9781493909940
OCLC Number: 881845237
Description: 1 online resource (x, 146 pages) : illustrations (some color).
Contents: 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.
Series Title: SpringerBriefs in quantitative finance
Responsibility: Pablo Azcue, Nora Muler.

Abstract:

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.

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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 Read more...

 
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