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Applied Stochastic Control of Jump Diffusions [electronic resource] / by Bernt Øksendal, Agnès Sulem.

Material type: TextSeries: Universitext: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005Description: X, 214 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540264415Additional physical formats: Printed edition:: No titleDDC classification: 519.2 LOC classification: QA273.A1-274.9QA274-274.9Online resources: Click here to access online
Contents:
Stochastic Calculus with Jump diffusions -- Optimal Stopping of Jump Diffusions -- Stochastic Control of Jump Diffusions -- Combined Optimal Stopping and Stochastic Control of Jump Diffusions -- Singular Control for Jump Diffusions -- Impulse Control of Jump Diffusions -- Approximating Impulse Control of Diffusions by Iterated Optimal Stopping -- Combined Stochastic Control and Impulse Control of Jump Diffusions -- Viscosity Solutions -- Solutions of Selected Exercises.
Summary: 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 (i.e. solutions of stochastic differential equations driven by Lévy processes) 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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Stochastic Calculus with Jump diffusions -- Optimal Stopping of Jump Diffusions -- Stochastic Control of Jump Diffusions -- Combined Optimal Stopping and Stochastic Control of Jump Diffusions -- Singular Control for Jump Diffusions -- Impulse Control of Jump Diffusions -- Approximating Impulse Control of Diffusions by Iterated Optimal Stopping -- Combined Stochastic Control and Impulse Control of Jump Diffusions -- Viscosity Solutions -- Solutions of Selected Exercises.

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 (i.e. solutions of stochastic differential equations driven by Lévy processes) 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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