Stochastic Optimization in Insurance: A Dynamic Programming Approach - Brossura
Libro 2 di 11: SpringerBriefs in Quantitative Finance
Sinossi
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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Recensione
“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)
Contenuti
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.
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 156 pp. Englisch. Codice articolo 9781493909940
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. A concise viscosity solution approach in insurance control problemsProvides existence and structure of optimal strategiesOffers systematic construction of the optimal value functionsThe main purpose of the book is to show how a v. Codice articolo 4213978
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 156 pp. Englisch. Codice articolo 9781493909940
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