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380 12. Gestion des risques grands et extrêmes and Finance (Springer, New York). Malevergne, Y. and D. Sornette (2001) General framework for a portfolio theory with non- Gaussian risks and non-linear correlations, paper presented at the 18th International conference in Finance, June 2001, Namur, Belgium (e-print at http : //arXiv.org/abs/cond−mat/0103020). Malevergne, Y. and D. Sornette (2002) Tail Dependence of Factor Models, working paper (http : //arXiv.org/abs/cond − mat/0202356). Johansen, A. et D. Sornette (2002), “Large Price Drawdowns Are Outliers”, Journal of Risk 4 (2), (http : //arXiv.org/abs/cond − mat/0010050). Sornette, D. (1999) Complexity, catastrophe and physics, Physics World 12 (N12), 57-57. Sornette, D. (2002) Predictability of catastrophic events : material rupture, earthquakes, turbulence, financial crashes and human birth, Proceedings of the National Academy of Sciences USA, vol. 4, (e-print at http : //arXiv.org/abs/cond − mat/0107173). Sornette, D., P. Simonetti and J. V. Andersen (2000) φ q -field theory for Portfolio optimization : ``fat tails” and non-linear correlations, Physics Report 335 (2), 19-92. Zajdenweber, D., Economie des extrêmes (Flammarion, 2000).
12.2. Minimiser l’impact des grands co-mouvements 381 12.2 Minimiser l’impact des grands co-mouvements A l’aide des résultats exposés au chapitre 9 section 9.2, nous montrons comment le coefficient de dépendance de queue entre un actif et un de ces facteurs explicatifs (le marché par exemple) ou entre deux actifs, peut facilement être calibré. Nous construisons ensuite des portefeuilles composés d’actifs ayant de très faibles coefficients de dépendance de queue avec le marché et montrons qu’ils présentent une corrélation remarquablement plus faible que des portefeuilles composés d’actifs ayant une plus forte dépendance de queue avec le marché, et ce sans dégradation de la performance mesurée par le ratio de Sharpe. Reprint from : Y. Malevergne et D.Sornette (2002), Minimizing extremes, RISK 15(11), 129-134.
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UNIVERSITE DE NICE-SOPHIA ANTIPOLIS
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4 Table des matières 2.2.2 Bulles
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6 Table des matières 7.3.2 Tests n
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8 Table des matières 12.1.1 Distri
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10 Table des matières Références
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12 m’ont souvent été d’un gra
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14 Introduction pour espérer se co
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16 Introduction les distributions e
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18 Introduction
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Chapitre 1 Faits stylisés des rent
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1.1. Rappel des faits stylisés 23
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1.1. Rappel des faits stylisés 25
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1.2. De la difficulté de représen
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1.3. Modélisation des propriétés
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Chapitre 2 Modèles phénoménologi
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2.1. Bulles rationnelles multi-dime
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2.2. Des bulles rationnelles aux kr
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Chapitre 3 Distributions exponentie
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Empirical Distributions of Log-Retu
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concerning tail fatness can be form
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To fit our two data sets, section 4
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properties, stressing the problems
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Another problem lies in the determi
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In order to obtain a process with S
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and Sornette (1999) for instance. W
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1. The Pareto distribution: 79 Fu(x
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empirical analog FN(x), estimated f
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have been chosen to converge to 1 a
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5 Comparison of the descriptive pow
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ased on the fact that the quantity
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tail (positive or negative) of the
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Equation (46) depends on c only and
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B Minimum Anderson-Darling Estimato
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C Local exponent In this Appendix,
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D Testing non-nested hypotheses wit
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where α = (c ∗ ,d ∗ ). It can
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where E0[·] denotes the expectatio
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References Andersen, J.V. and D. So
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Gouriéroux C. and A. Monfort, 1994
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Rubinstein, M., 1973, The fundament
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(a) Independent Data Stretched-Expo
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(a) Dow Jones Positive Tail Negativ
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Nasdaq Dow Jones Pos. Tail Neg. Tai
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Dow Jones positive tail Dow Jones n
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Variation coefficient Variation coe
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Mean excess function Mean excess fu
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Hill‘s estimate b u Hill‘s esti
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Wilks statistic (doubled log−like
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Tail 1−F(x) and parameter b Tail
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1.4 1.2 1 0.8 0.6 0.4 0.2 0 1 2 3 4
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Chapitre 4 Relaxation de la volatil
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Volatility Fingerprints of Large Sh
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2 Long-range memory and distinction
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Figure 2: Measuring the conditional
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the system to the accumulation of m
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Appendix C: “Conditional response
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Baillie, R.T., 1996, Long memory pr
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Chapitre 5 Approche comportementale
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5.1. Prix d’un actif et excès de
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5.2. Modèles d’opinion contre mo
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5.4. Conséquences des phénomènes
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5.5. Conclusion 157 ce qui induit u
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Chapitre 6 Comportements mimétique
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RESEARCH PAPER Q UANTITATIVE F INAN
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A Corcos et al Q UANTITATIVE F INAN
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Deuxième partie Etude des proprié
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182 7. Etude de la dépendance à l
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192 8. Tests de copule gaussienne
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194 8. Tests de copule gaussienne 1
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200 8. Tests de copule gaussienne t
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202 8. Tests de copule gaussienne T
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204 8. Tests de copule gaussienne a
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206 8. Tests de copule gaussienne c
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208 8. Tests de copule gaussienne t
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210 8. Tests de copule gaussienne (
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212 8. Tests de copule gaussienne R
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228 8. Tests de copule gaussienne f
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236 8. Tests de copule gaussienne T
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238 9. Mesure de la dépendance ext
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Page 347 and 348: 10.1. La théorie de l’utilité 3
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Page 361 and 362: 10.4. Conclusion 361 et de manière
Page 363 and 364: Chapitre 11 Portefeuilles optimaux
Page 365 and 366: 11.2. Prise en compte des grands ri
Page 367 and 368: 11.3. Equilibre de marché 367 s’
Page 369 and 370: 11.5. Annexe 369 Collective Origin
Page 371 and 372: 11.5. Annexe 371 point λ = 1. Thus
Page 373 and 374: Chapitre 12 Gestion des risques gra
Page 375 and 376: 12.1. Comprendre et gérer les risq
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Page 387 and 388: Chapitre 13 Gestion de portefeuille
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Page 393 and 394: given a series of return {rt}t foll
Page 395 and 396: eads cV (u1, · · · , un) = 1
Page 397 and 398: THEOREM 4 (TAIL EQUIVALENCE FOR A S
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Page 401 and 402: 3.2 Typical recurrence time of larg
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Page 407 and 408: Choosing x > y > Aɛ, and applying
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Page 413 and 414: B Asymptotic distribution of the su
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This property is verified for all c
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µn=α of order n = 2, 4, 6 and 8.
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these two assets or portfolios. The
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Due to the homogeneity property of
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invested in the risky fund depends
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C. Then, if g1(X1), · · · , gn(X
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Differentiating with respect to x1,
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7.2 Transformation of the modified
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In the sequel, we will first evalua
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8.3 Non-symmetric assets In the cas
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y the variance will then increase).
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A Description of the data set We ha
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thus and finally 1 λ1 n−1 = w
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C Composition of the market portfol
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D Generalized capital asset princin
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This brings us back to the problem
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F.2 General case We now consider a
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Harvey, C.R. and A. Siddique, 2000,
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µ µ2 1/2 µ4 1/4 µ6 1/6 µ8 1/8
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Mean (10 −3 ) Variance (10 −3 )
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μ (daily return) x 10−3 2.5 2 1.
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w i w i 0.2 0.15 0.1 0.05 Mean−μ
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Figure 6: Schematic representation
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Empirical Cumulative Distribution 1
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Z 2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0
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Z 2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0
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10 0 10 −1 10 0 10 −1 10 −1 1
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10 0 10 −1 10 0 10 −1 10 −1 1
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κ 22 20 18 16 14 12 10 8 6 4 2 Exc
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Return μ 0.12 0.11 0.1 0.09 0.08 0
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Conclusions et Perspectives L’obj
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Conclusion 493 en univers gaussien
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Annexe A Evaluation de la conduite
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A.2. Eléments de contexte 497 bora
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A.4. Compétences acquises et ensei
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A.5. Conclusion 501 de la recherche
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Bibliographie ACERBI, C. (2002) :
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Bibliographie 505 BOUCHAUD, J. P. E
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Bibliographie 507 DE FINETTI, B. (1
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Bibliographie 509 GRANGER, C. W. ET
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Bibliographie 511 LILLO, F. ET R. N
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Bibliographie 513 PATTON, A. (2001)
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Bibliographie 515 SUSMEL, R. (1996)
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