Ebook: Applied Stochastic Control of Jump Diffusions
- Tags: Operations Research Mathematical Programming, Operator Theory, Quantitative Finance, Probability Theory and Stochastic Processes
- Series: Universitext
- Year: 2005
- Publisher: Springer Berlin Heidelberg
- Language: English
- pdf
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 L?vy 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.
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 L?vy 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.
Content:
Front Matter....Pages III-X
Stochastic Calculus with Jump diffusions....Pages 1-25
Optimal Stopping of Jump Diffusions....Pages 27-37
Stochastic Control of Jump Diffusions....Pages 39-58
Combined Optimal Stopping and Stochastic Control of Jump Diffusions....Pages 59-70
Singular Control for Jump Diffusions....Pages 71-80
Impulse Control of Jump Diffusions....Pages 81-95
Approximating Impulse Control of Diffusions by Iterated Optimal Stopping....Pages 97-112
Combined Stochastic Control and Impulse Control of Jump Diffusions....Pages 113-122
Viscosity Solutions....Pages 123-147
Solutions of Selected Exercises....Pages 149-196
Back Matter....Pages 197-212
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 L?vy 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.
Content:
Front Matter....Pages III-X
Stochastic Calculus with Jump diffusions....Pages 1-25
Optimal Stopping of Jump Diffusions....Pages 27-37
Stochastic Control of Jump Diffusions....Pages 39-58
Combined Optimal Stopping and Stochastic Control of Jump Diffusions....Pages 59-70
Singular Control for Jump Diffusions....Pages 71-80
Impulse Control of Jump Diffusions....Pages 81-95
Approximating Impulse Control of Diffusions by Iterated Optimal Stopping....Pages 97-112
Combined Stochastic Control and Impulse Control of Jump Diffusions....Pages 113-122
Viscosity Solutions....Pages 123-147
Solutions of Selected Exercises....Pages 149-196
Back Matter....Pages 197-212
....