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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