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Title:
Applied stochastic control of jump diffusions
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New York, NY : Springer, 2005
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9783540140238
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30000004598607 QA402.37 O37 2005 Open Access Book Book
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Table of Contents

1 Stochastic Calculus with Jump diffusionsp. 1
1.1 Basic definitions and results on Levy Processesp. 1
1.2 The Ito formula and related resultsp. 5
1.3 Levy stochastic differential equationsp. 10
1.4 The Girsanov theorem and applicationsp. 12
1.5 Application to financep. 19
1.6 Exercisesp. 22
2 Optimal Stopping of Jump Diffusionsp. 27
2.1 A general formulation and a verification theoremp. 27
2.2 Applications and examplesp. 31
2.3 Exercisesp. 36
3 Stochastic Control of Jump Diffusionsp. 39
3.1 Dynamic programmingp. 39
3.2 The maximum principlep. 46
3.3 Application to financep. 52
3.4 Exercisesp. 55
4 Combined Optimal Stopping and Stochastic Control of Jump Diffusionsp. 59
4.1 Introductionp. 59
4.2 A general mathematical formulationp. 60
4.3 Applicationsp. 65
4.4 Exercisesp. 69
5 Singular Control for Jump Diffusionsp. 71
5.1 An illustrating examplep. 71
5.2 A general formulationp. 73
5.3 Application to portfolio optimization with transaction costsp. 76
5.4 Exercisesp. 78
6 Impulse Control of Jump Diffusionsp. 81
6.1 A general formulation and a verification theoremp. 81
6.2 Examplesp. 85
6.3 Exercicesp. 94
7 Approximating Impulse Control of Diffusions by Iterated Optimal Stoppingp. 97
7.1 Iterative schemep. 97
7.2 Examplesp. 107
7.3 Exercicesp. 112
8 Combined Stochastic Control and Impulse Control of Jump Diffusionsp. 113
8.1 A verification theoremp. 113
8.2 Examplesp. 116
8.3 Iterative methodsp. 120
8.4 Exercicesp. 122
9 Viscosity Solutionsp. 123
9.1 Viscosity solutions of variational inequalitiesp. 124
9.2 The value function is not always C 1p. 127
9.3 Viscosity solutions of HJBQVIp. 130
9.4 Numerical analysis of HJBQVIp. 140
9.5 Exercisesp. 146
10 Solutions of Selected Exercisesp. 149
10.1 Exercises of Chapter 1p. 149
10.2 Exercises of Chapter 2p. 153
10.3 Exercises of Chapter 3p. 162
10.4 Exercises of Chapter 4p. 169
10.5 Exercises of Chapter 5p. 171
10.6 Exercises of Chapter 6p. 174
10.7 Exercises of Chapter 7p. 185
10.8 Exercises of Chapter 8p. 188
10.9 Exercises of Chapter 9p. 191
Referencesp. 197
Notation and Symbolsp. 203
Indexp. 207