APPLIED STOCHASTIC CONTROL OF JUMP DIFFUSIONS B.OKSENDAL,A.SULEM Księgarnia

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.

Written for: Students and lecturers in stochastic control of jump diffusions, verifications theorems, and applications to finance

Keywords:

Lévy processes

impulse control

jump diffusions

stochastic control

Stochastic Calculus with Jump di.usions . .

1.1 Basic de.nitions and results on L'evy Processes . .

1.2 The It'o formula and related results .

1.3 L´evy stochastic di.erential equations .

1.4 The Girsanov theorem and applications .

1.5 Application to .nance .

1.6 Exercises .

2 Optimal Stopping of Jump Di.usions

2.1 A general formulation and a veri.cation theorem .

2.2 Applications and examples.

2.3 Exercises .

3 Stochastic Control of Jump Di.usions .

3.1 Dynamic programming . .

3.2 The maximum principle .

3.3 Application to .nance .

3.4 Exercises .

4 Combined Optimal Stopping and Stochastic Control of Jump Di.usions .

4.1 Introduction .

4.2 A general mathematical formulation .

4.3 Applications .

4.4 Exercises .

5 Singular Control for Jump Di.usions .

5.1 An illustrating example

5.2 A general formulation .

5.3 Application to portfolio optimization with transaction costs .

5.4 Exercises .

X Contents

6 Impulse Control of Jump Di.usions .

6.1 A general formulation and a veri.cation theorem .

6.2 Examples.

6.3 Exercices .

7 Approximating Impulse Control of Di.usions by Iterated Optimal Stopping.

7.1 Iterative scheme .

7.2 Examples.

7.3 Exercices .

8 Combined Stochastic Control and Impulse Control of Jump Di.usions .

8.1 A veri.cation theorem .

8.2 Examples.

8.3 Iterative methods.

8.4 Exercices .

9 Viscosity Solutions .

9.1 Viscosity solutions of variational inequalities .

9.2 The value function is not always C1 .

9.3 Viscosity solutions of HJBQVI .

9.4 Numerical analysis of HJBQVI .

9.5 Exercises .

10 Solutions of Selected Exercises .

10.1 Exercises of Chapter 1 .

10.2 Exercises of Chapter 2 .

10.3 Exercises of Chapter 3 .

10.4 Exercises of Chapter 4 .

10.5 Exercises of Chapter 5 .

10.6 Exercises of Chapter 6 .

10.7 Exercises of Chapter 7 .

10.8 Exercises of Chapter 8 .

10.9 Exercises of Chapter 9 .

References .

Notation and Symbols .

Index

208 pages softcover

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czy wybrany tytuł polskojęzyczny lub anglojęzyczny jest aktualnie na półce księgarni.