Stochastic Control in Insurance
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Beschreibung
Stochastic control is one of the methods being used to find optimal decision-making strategies in fields such as operations research and mathematical finance. In recent years, stochastic control techniques have been applied to non-life insurance problems, and in life insurance the theory has been further developed.
This book provides a systematic treatment of optimal control methods applied to problems from insurance and investment, complete with detailed proofs. The theory is discussed and illustrated by way of examples, using concrete simple optimisation problems that occur in the actuarial sciences. The problems come from non-life insurance as well as life and pension insurance and also cover the famous Merton problem from mathematical finance. Wherever possible, the proofs are probabilistic but in some cases well-established analytical methods are used.
The book is directed towards graduate students and researchers in actuarial science and mathematical finance who want to learn stochastic control within an insurance setting, but it will also appeal to applied probabilists interested in the insurance applications and to practitioners who want to learn more about how the method works.
Readers should be familiar with basic probability theory and have a working knowledge of Brownian motion, Markov processes, martingales and stochastic calculus. Some knowledge of measure theory will also be useful for following the proofs.
Until now, solved examples of the application of stochastic control to actuarial problems could only be found in journals - this is the first book to systematically present these methods in one volume. The author starts with a short introduction to stochastic control techniques. Then he applies the principles to several problems in actuarial mathematics. These examples show how verification theorems and existence theorems may be proved - they also show that, in contrast to general belief, the non-diffusion case is simpler than the diffusion case. In the last part of the book, applied probability techniques are used to determine the asymptotics of the controlled stochastic process. This book also includes a number of appendices to supplement the main material of the book - and will be suitable for graduate and postgraduate students of actuarial and financial mathematics, as well as researchers, and practitioners in insurance companies and banks who wish to use these techniques in their work.
First systematic treatment of actuarial control, rather than financial control The area has developed considerably in recent years, and results are collected here in one volume for the first time Approaches stochastic control theory for specific examples motivated by problems in actuarial mathematics - readers will be able to see the theory work
Autor*in
Hanspeter Schmidli
Themen in »Stochastic Control in Insurance«
Control Investment Optimal control Probability theory calculus insurance life insurance measure theory non-life insurance optimal control methods probability proof stochastic control theorem
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From the reviews:
"This book provides a state of the art treatment of dynamic stochastic control problems arising in insurance, like investment, dividend payout and reinsurance problems. … The book comprises four chapters and a comprehensive appendix about stochastic processes, risk theory, life insurance and the Black-Scholes model. … is certainly a valuable reference for graduate students and researchers in actuarial sciences who are interested in stochastic control methods. It discusses in a critical way the HJB approach for these problems and shows its scope and limitations." (Nicole Bäuerle, Mathematical Reviews, Issue 2008 k)
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