Title:
Applied stochastic control of jump diffusions
Personal Author:
Publication Information:
New York, NY : Springer, 2005
ISBN:
9783540140238
General Note:
Also available online version
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Electronic Access:
Full Text
DSP_RESTRICTION_NOTE:
Accessible within UTM campus
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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
---|---|---|---|---|---|
Searching... | 30000004598607 | QA402.37 O37 2005 | Open Access Book | Book | Searching... |
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Table of Contents
1 Stochastic Calculus with Jump diffusions | p. 1 |
1.1 Basic definitions and results on Levy Processes | p. 1 |
1.2 The Ito formula and related results | p. 5 |
1.3 Levy stochastic differential equations | p. 10 |
1.4 The Girsanov theorem and applications | p. 12 |
1.5 Application to finance | p. 19 |
1.6 Exercises | p. 22 |
2 Optimal Stopping of Jump Diffusions | p. 27 |
2.1 A general formulation and a verification theorem | p. 27 |
2.2 Applications and examples | p. 31 |
2.3 Exercises | p. 36 |
3 Stochastic Control of Jump Diffusions | p. 39 |
3.1 Dynamic programming | p. 39 |
3.2 The maximum principle | p. 46 |
3.3 Application to finance | p. 52 |
3.4 Exercises | p. 55 |
4 Combined Optimal Stopping and Stochastic Control of Jump Diffusions | p. 59 |
4.1 Introduction | p. 59 |
4.2 A general mathematical formulation | p. 60 |
4.3 Applications | p. 65 |
4.4 Exercises | p. 69 |
5 Singular Control for Jump Diffusions | p. 71 |
5.1 An illustrating example | p. 71 |
5.2 A general formulation | p. 73 |
5.3 Application to portfolio optimization with transaction costs | p. 76 |
5.4 Exercises | p. 78 |
6 Impulse Control of Jump Diffusions | p. 81 |
6.1 A general formulation and a verification theorem | p. 81 |
6.2 Examples | p. 85 |
6.3 Exercices | p. 94 |
7 Approximating Impulse Control of Diffusions by Iterated Optimal Stopping | p. 97 |
7.1 Iterative scheme | p. 97 |
7.2 Examples | p. 107 |
7.3 Exercices | p. 112 |
8 Combined Stochastic Control and Impulse Control of Jump Diffusions | p. 113 |
8.1 A verification theorem | p. 113 |
8.2 Examples | p. 116 |
8.3 Iterative methods | p. 120 |
8.4 Exercices | p. 122 |
9 Viscosity Solutions | p. 123 |
9.1 Viscosity solutions of variational inequalities | p. 124 |
9.2 The value function is not always C 1 | p. 127 |
9.3 Viscosity solutions of HJBQVI | p. 130 |
9.4 Numerical analysis of HJBQVI | p. 140 |
9.5 Exercises | p. 146 |
10 Solutions of Selected Exercises | p. 149 |
10.1 Exercises of Chapter 1 | p. 149 |
10.2 Exercises of Chapter 2 | p. 153 |
10.3 Exercises of Chapter 3 | p. 162 |
10.4 Exercises of Chapter 4 | p. 169 |
10.5 Exercises of Chapter 5 | p. 171 |
10.6 Exercises of Chapter 6 | p. 174 |
10.7 Exercises of Chapter 7 | p. 185 |
10.8 Exercises of Chapter 8 | p. 188 |
10.9 Exercises of Chapter 9 | p. 191 |
References | p. 197 |
Notation and Symbols | p. 203 |
Index | p. 207 |