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Author(s): | Bernt Øksendal, Agnès Sulem | |||
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Publisher: | Springer | |||
Year: | 2007 | |||
Language: | English | |||
Pages: | 214 pages | |||
Size: | 1.29 MB | |||
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[content title="Description"]The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. The types of control problems covered include classical stochastic control, optimal stopping, impulse control and singular control. Both the dynamic programming method and the maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton-Jacobi Bellman equation and/or (quasi-)variational inequalities are formulated. There are also chapters on the viscosity solution formulation and numerical methods. The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end of each chapter with complete solutions. This will help the reader understand the theory and see how to apply it. The book assumes some basic knowledge of stochastic analysis, measure theory and partial differential equations.
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[content title="About the author"]Bernt Karsten Øksendal (born 10 April 1945 in Fredrikstad) is a Norwegian mathematician. He completed his undergraduate studies at the University of Oslo, working under Otte Hustad. He obtained his PhD from University of California, Los Angeles in 1971; his thesis was titled Peak Sets and Interpolation Sets for Some Algebras of Analytic Functions and was supervised by Theodore Gamelin. In 1991, he was appointed as a professor at the University of Oslo. In 1992, he was appointed as an adjunct professor at the Norwegian School of Economics and Business Administration, Bergen, Norway.
His main field of interest is stochastic analysis, including stochastic control, optimal stopping, stochastic ordinary and partial differential equations and applications, particularly to physics, biology and finance. For his contributions to these fields, he was awarded the Nansen Prize in 1996. He has been a member of the Norwegian Academy of Science and Letters since 1996. He was elected as a member of the Norwegian Royal Society of Sciences in 2002.Agnès Sulem (born 1959)[1] is a French applied mathematician whose research topics include stochastic control, jump diffusion, and mathematical finance.
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