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194 BIBLIOGRAPHY [57] P. Jorion, On jump processes in the foreign exchange and stock markets, Rev. Fin. Studies, 1 (1988), pp. 427–445. [58] J. Kallsen, Utility-based derivative pricing, in Mathematical Finance — Bachelier Congress 2000, Springer, Berlin, 2001. [59] J. Kallsen and P. Tankov, Characterization of dependence of multidimensional Lévy processes using Lévy copulas. Preprint, available from www.cmap.polytechnique.fr/~tankov, 2004. [60] J. F. C. Kingman and S. J. Taylor, Introduction to Measure and Probability, Cambridge University Press, Cambridge, 1966. [61] I. Koponen, Analytic approach to the problem of convergence of truncated Lévy flights towards the Gaussian stochastic process., Physical Review E, 52 (1995), pp. 1197–1199. [62] S. Kou, A jump-diffusion model for option pricing, Management Science, 48 (2002), pp. 1086–1101. [63] R. W. Lee, Option pricing by transform methods: extensions, unification and error control, J. Comput. Finance, 7 (2004). [64] A. Lindner and A. Szimayer, A limit theorem for copulas. Download from www-m4.ma.tum.de/m4/pers/lindner, 2003. [65] F. Lindskog and A. McNeil, Common Poisson shock models: Applications to insurance and credit risk modelling. Available from www.risklab.ch, September 2001. [66] D. Madan, Financial modeling with discontinuous price processes, in Lévy Processes — Theory and Applications, O. Barndorff-Nielsen, T. Mikosch, and S. Resnick, eds., Birkhäuser, Boston, 2001. [67] D. Madan, P. Carr, and E. Chang, The variance gamma process and option pricing, European Finance Review, 2 (1998), pp. 79–105. [68] D. Madan and M. Konikov, Option pricing using variance gamma Markov chains, Rev. Derivatives Research, 5 (2002), pp. 81–115.
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Thèse présentée pour obtenir le
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Abstract This thesis deals with the
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Contents Remarks on notation 11 Int
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CONTENTS 9 II Multidimensional mode
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12 For {P n } n≥1 , P ∈ P(Ω) t
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14 INTRODUCTION EN FRANCAIS corresp
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16 INTRODUCTION EN FRANCAIS Lévy p
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18 INTRODUCTION EN FRANCAIS Calibra
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20 INTRODUCTION EN FRANCAIS • Si
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22 INTRODUCTION EN FRANCAIS et Scai
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24 INTRODUCTION EN FRANCAIS Ce rés
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26 INTRODUCTION EN FRANCAIS dans un
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28 INTRODUCTION 7500 Taux de change
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30 INTRODUCTION Lévy models by Fou
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Chapter 1 Lévy processes and exp-L
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1.1. LEVY PROCESSES 35 Proposition
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1.1. LEVY PROCESSES 37 The characte
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1.1. LEVY PROCESSES 39 On the other
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1.2. EXPONENTIAL LEVY MODELS 41 (b)
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1.3. EXP-LEVY MODELS IN FINANCE 43
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1.3. EXP-LEVY MODELS IN FINANCE 45
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1.4. PRICING EUROPEAN OPTIONS 47 wi
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1.4. PRICING EUROPEAN OPTIONS 49 Pr
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1.4. PRICING EUROPEAN OPTIONS 51 Nu
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1.4. PRICING EUROPEAN OPTIONS 53 By
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1.4. PRICING EUROPEAN OPTIONS 55 Si
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Chapter 2 The calibration problem a
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2.1. LEAST SQUARES CALIBRATION 59 m
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2.1. LEAST SQUARES CALIBRATION 61 i
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2.1. LEAST SQUARES CALIBRATION 63 w
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2.1. LEAST SQUARES CALIBRATION 65 A
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2.1. LEAST SQUARES CALIBRATION 67 i
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2.2. SELECTION USING RELATIVE ENTRO
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2.2. SELECTION USING RELATIVE ENTRO
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2.3. RELATIVE ENTROPY IN THE LITERA
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2.4. RELATIVE ENTROPY OF LEVY PROCE
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2.4. RELATIVE ENTROPY OF LEVY PROCE
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2.5. REGULARIZING THE CALIBRATION P
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Chapter 3 Numerical implementation
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3.1. DISCRETIZING THE CALIBRATION P
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3.2. CHOICE OF THE PRIOR 99 Since
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3.2. CHOICE OF THE PRIOR 101 twice
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3.3. CHOICE OF THE REGULARIZATION P
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3.4. CHOICE OF THE WEIGHTS 111 Then
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3.5. NUMERICAL SOLUTION 113 have th
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3.5. NUMERICAL SOLUTION 115 of X t
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3.5. NUMERICAL SOLUTION 117 since
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3.6. NUMERICAL AND EMPIRICAL TESTS
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Part II Multidimensional modelling
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134 CHAPTER 4. DEPENDENCE OF LEVY P
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Page 144 and 145: 144 CHAPTER 4. DEPENDENCE OF LEVY P
Page 166 and 167: 166 CHAPTER 5. APPLICATIONS OF LEVY
Page 188 and 189: 188 CONCLUSIONS AND PERSPECTIVES ge
Page 190 and 191: 190 BIBLIOGRAPHY [9] O. E. Barndorf
Page 192 and 193: 192 BIBLIOGRAPHY [33] F. Delbaen, P
Page 196 and 197: 196 BIBLIOGRAPHY [81] S. Raible, L
Page 198 and 199: 198 BIBLIOGRAPHY
Page 200: 200 INDEX tightness, 40 levycalibra
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