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196 BIBLIOGRAPHY [81] S. Raible, Lévy Processes in Finance: Theory, Numerics and Empirical Facts, PhD thesis, Freiburg University, 1998. [82] S. I. Resnick, Extreme Values, Regular Variation and Point Processes, Springer-Verlag, 1987. [83] R. T. Rockafellar, Integrals which are convex functionals, Pacific journal of mathematics, 24 (1968), pp. 525–539. [84] J. Rosiński, Series representations of Lévy processes from the perspective of point processes, in Lévy Processes — Theory and Applications, O. Barndorff-Nielsen, T. Mikosch, and S. Resnick, eds., Birkhäuser, Boston, 2001. [85] M. Rubinstein, Implied binomial trees, Journal of Finance, 49 (1994), pp. 771–819. [86] T. H. Rydberg, The normal inverse Gaussian Lévy process: simulation and approximation, Comm. Statist. Stochastic Models, 13 (1997), pp. 887–910. [87] K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge, UK, 1999. [88] B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North Holland, 1983. [89] M. Schweizer, On the minimal martingale measure and the Föllmer-Schweizer decomposition, Stochastic Anal. Appl., 13 (1995), pp. 573–599. [90] A. Sklar, Random variables, distribution functions, and copulas — a personal look backward and forward, in Distributions with Fixed Marginals and Related Topics, L. Rüschendorf, B. Schweizer, and M. D. Taylor, eds., Institute of Mathematical Statistics, Hayward, CA, 1996. [91] M. Stutzer, A simple nonparametric approach to derivative security valuation, Journal of Finance, 51 (1996), pp. 1633–1652. [92] P. Tankov, Dependence structure of spectrally positive multidimensional Lévy processes. Download from www.cmap.polytechnique.fr/~tankov, 2003.
BIBLIOGRAPHY 197 [93] M. Teboulle and I. Vajda, Convergence of best φ-entropy estimates, IEEE transactions on information theory, 39 (1993), pp. 297–301. [94] A. N. Tikhonov and V. Arsenin, Solutions of Ill-Posed Problems, Wiley, New York, 1977. [95] A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems, Kluwer Academic Publishers, 1995. [96] X. Zhang, Analyse Numérique des Options Américaines dans un Modèle de Diffusion avec Sauts, PhD thesis, Ecole Nationale des Ponts et Chaussées, 1994.
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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 146 and 147: 146 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 194 and 195: 194 BIBLIOGRAPHY [57] P. Jorion, On
Page 198 and 199: 198 BIBLIOGRAPHY
Page 200: 200 INDEX tightness, 40 levycalibra
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