Processus de LÃ©vy en Finance - Laboratoire de ProbabilitÃ©s et ...

More documents

Recommendations

Info

192 BIBLIOGRAPHY [33] F. Delbaen, P. Grandits, T. Rheinländer, D. Samperi, M. Schweizer, and C. Stricker, Exponential hedging and entropic penalties, Math. Finance, 12 (2002), pp. 99–123. [34] F. Delbaen and W. Schachermayer, The fundamental theorem of asset pricing for unbounded stochastic processes, Math. Ann., 312 (1998), pp. 215–250. [35] B. Dupire, Pricing with a smile, RISK, 7 (1994), pp. 18–20. [36] E. Eberlein, Applications of generalized hyperbolic Lévy motion to Finance, in Lévy Processes — Theory and Applications, O. Barndorff-Nielsen, T. Mikosch, and S. Resnick, eds., Birkhäuser, Boston, 2001, pp. 319–336. [37] E. Eberlein, U. Keller, and K. Prause, New insights into smile, mispricing and Value at Risk: The hyperbolic model, Journal of Business, 71 (1998), pp. 371–405. [38] E. Eberlein and S. Raible, Some analytic facts on the generalized hyperbolic model, in European Congress of Mathematics, Vol. II (Barcelona, 2000), vol. 202 of Progr. Math., Birkhäuser, Basel, 2001, pp. 367–378. [39] N. El Karoui and R. Rouge, Pricing via utility maximization and entropy, Math. Finance, 10 (2000), pp. 259–276. [40] H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems, vol. 375, Kluwer Academic Publishers Group, Dordrecht, 1996. [41] H. Föllmer and M. Schweizer, Hedging of contingent claims under incomplete information, in Applied Stochastic Analysis, M. Davis and R. Elliott, eds., vol. 5, Gordon and Breach, London, 1991, pp. 389–414. [42] M. Frittelli, The minimal entropy martingale measure and the valuation problem in incomplete markets, Math. Finance, 10 (2000), pp. 39–52. [43] H. Geman, Pure jump Lévy processes for asset price modeling, Journal of Banking and Finance, 26 (2002), pp. 1297–1316. [44] H. Geman, D. Madan, and M. Yor, Time changes for Lévy processes, Math. Finance, 11 (2001), pp. 79–96.
BIBLIOGRAPHY 193 [45] P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, New York, 2003. [46] P. Glasserman and B. Yu, Large sample properties of weighted Monte Carlo estimators. Preprint, available from www.gsb.columbia.edu/faculty/pglasserman/Other/, 2002. [47] T. Goll and J. Kallsen, Optimal portfolios for logarithmic utility, Stochastic Process. Appl., 89 (2000), pp. 31–48. [48] T. Goll and L. Rüschendorf, Minimal distance martingale measures and optimal portfolios consistent with observed market prices. Preprint, available from www.stochastik.uni-freiburg.de/~goll/start.html, 2000. [49] , Minimax and minimal distance martingale measures and their relationship to portfolio optimization, Finance Stoch., 5 (2001), pp. 557–581. [50] A. V. Goncharsky, A. S. Leonov, and A. G. Yagola, Applicability of the disparity principle in the case of non-linear incorrectly posed problems, and a new regularizing algorithm for solving them, USSR Comp. Math. Math. Phys, 15 (1975), pp. 8–16. [51] C. Gouriéroux and A. Monfort, Simulation-Based Econometric Methods, Oxford University Press, 1996. [52] A. Hobson, Concepts in Statistical Mechanics, Gordon and Breach, Langhorne, Pennsylvania, 1971. [53] N. Jackson, E. Süli, and S. Howison, Computation of deterministic volatility surfaces, Journal of Computational Finance, 2 (1999), pp. 5–32. [54] J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes, Springer, Berlin, 2nd ed., 2003. [55] P. Jakubenas, On option pricing in certain incomplete markets, Proceedings of the Steklov Mathematical Institute, 237 (2002). [56] H. Joe, Multivariate Models and Dependence Concepts, Chapman & Hall, London, 1997.
Page 1 and 2:
Thèse présentée pour obtenir le
Page 3:
Abstract This thesis deals with the
Page 7 and 8:
Contents Remarks on notation 11 Int
Page 9:
CONTENTS 9 II Multidimensional mode
Page 12 and 13:
12 For {P n } n≥1 , P ∈ P(Ω) t
Page 14 and 15:
14 INTRODUCTION EN FRANCAIS corresp
Page 16 and 17:
16 INTRODUCTION EN FRANCAIS Lévy p
Page 18 and 19:
18 INTRODUCTION EN FRANCAIS Calibra
Page 20 and 21:
20 INTRODUCTION EN FRANCAIS • Si
Page 22 and 23:
22 INTRODUCTION EN FRANCAIS et Scai
Page 24 and 25:
24 INTRODUCTION EN FRANCAIS Ce rés
Page 26 and 27:
26 INTRODUCTION EN FRANCAIS dans un
Page 28 and 29:
28 INTRODUCTION 7500 Taux de change
Page 30 and 31:
30 INTRODUCTION Lévy models by Fou
Page 33 and 34:
Chapter 1 Lévy processes and exp-L
Page 35 and 36:
1.1. LEVY PROCESSES 35 Proposition
Page 37 and 38:
1.1. LEVY PROCESSES 37 The characte
Page 39 and 40:
1.1. LEVY PROCESSES 39 On the other
Page 41 and 42:
1.2. EXPONENTIAL LEVY MODELS 41 (b)
Page 43 and 44:
1.3. EXP-LEVY MODELS IN FINANCE 43
Page 45 and 46:
1.3. EXP-LEVY MODELS IN FINANCE 45
Page 47 and 48:
1.4. PRICING EUROPEAN OPTIONS 47 wi
Page 49 and 50:
1.4. PRICING EUROPEAN OPTIONS 49 Pr
Page 51 and 52:
1.4. PRICING EUROPEAN OPTIONS 51 Nu
Page 53 and 54:
1.4. PRICING EUROPEAN OPTIONS 53 By
Page 55 and 56:
1.4. PRICING EUROPEAN OPTIONS 55 Si
Page 57 and 58:
Chapter 2 The calibration problem a
Page 59 and 60:
2.1. LEAST SQUARES CALIBRATION 59 m
Page 61 and 62:
2.1. LEAST SQUARES CALIBRATION 61 i
Page 63 and 64:
2.1. LEAST SQUARES CALIBRATION 63 w
Page 65 and 66:
2.1. LEAST SQUARES CALIBRATION 65 A
Page 67 and 68:
2.1. LEAST SQUARES CALIBRATION 67 i
Page 69 and 70:
2.2. SELECTION USING RELATIVE ENTRO
Page 71 and 72:
2.2. SELECTION USING RELATIVE ENTRO
Page 73 and 74:
2.3. RELATIVE ENTROPY IN THE LITERA
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
2.4. RELATIVE ENTROPY OF LEVY PROCE
Page 83 and 84:
2.4. RELATIVE ENTROPY OF LEVY PROCE
Page 85 and 86:
2.5. REGULARIZING THE CALIBRATION P
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Chapter 3 Numerical implementation
Page 97 and 98:
3.1. DISCRETIZING THE CALIBRATION P
Page 99 and 100:
3.2. CHOICE OF THE PRIOR 99 Since
Page 101 and 102:
3.2. CHOICE OF THE PRIOR 101 twice
Page 103 and 104:
3.3. CHOICE OF THE REGULARIZATION P
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
3.4. CHOICE OF THE WEIGHTS 111 Then
Page 113 and 114:
3.5. NUMERICAL SOLUTION 113 have th
Page 115 and 116:
3.5. NUMERICAL SOLUTION 115 of X t
Page 117 and 118:
3.5. NUMERICAL SOLUTION 117 since
Page 119 and 120:
3.6. NUMERICAL AND EMPIRICAL TESTS
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131:
Part II Multidimensional modelling
Page 134 and 135:
134 CHAPTER 4. DEPENDENCE OF LEVY P
Page 136 and 137:
Page 138 and 139:
Page 140 and 141:
Page 142 and 143: 142 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 194 and 195: 194 BIBLIOGRAPHY [57] P. Jorion, On
Page 196 and 197: 196 BIBLIOGRAPHY [81] S. Raible, L
Page 198 and 199: 198 BIBLIOGRAPHY
Page 200: 200 INDEX tightness, 40 levycalibra
show all

Processus de LÃ©vy en Finance - Laboratoire de ProbabilitÃ©s et ...

Create successful ePaper yourself

Delete template?

Save as template?