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420 13. Gestion de portefeuille sous contraintes de capital économique Gaussian Returns 10 1 10 0 10 −1 10 −4 10 −3 Standard & Poor’s 500 Raw Returns c/2 = 0.73 Figure 1: Graph of the Gaussianized Standard & Poor’s 500 index returns versus its raw returns, during the time interval from January 03, 1995 to December 29, 2000 for the negative tail of the distribution. 32 10 −2 10 −1
ln(T/T 0 ) T Figure 2: Logarithm ln of the ratio of the recurrence time T to a reference time T0 for the recurrence T0 of a given loss V aR as a function of β defined by β = VaR VaR∗ . VaR∗ (resp. VaR) is the Value-at-Risk over a time interval T0 (resp. T ). α 33 c>1 c=1 c
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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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Chapitre 10 La mesure du risque Dan
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10.1. La théorie de l’utilité 3
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10.2. Les mesures de risque cohére
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10.3. Les mesures de fluctuations 3
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10.4. Conclusion 361 et de manière
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Chapitre 11 Portefeuilles optimaux
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11.2. Prise en compte des grands ri
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11.3. Equilibre de marché 367 s’
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Page 375 and 376: 12.1. Comprendre et gérer les risq
Page 381 and 382: 12.2. Minimiser l’impact des gran
Page 387 and 388: Chapitre 13 Gestion de portefeuille
Page 389 and 390: VaR-Efficient Portfolios for a Clas
Page 391 and 392: dependence: from independence to co
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
Page 399 and 400: Independent Assets Comonotonic Asse
Page 401 and 402: 3.2 Typical recurrence time of larg
Page 403 and 404: and finally w ∗ i = χ−1 i j
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Page 407 and 408: Choosing x > y > Aɛ, and applying
Page 409 and 410: Expanding fi(xi) around x ∗ i yie
Page 411 and 412: for all h ∈ AC. Thus, integrating
Page 413 and 414: B Asymptotic distribution of the su
Page 415 and 416: This yields × h+ Sc−2 − 2 dh
Page 417 and 418: References Acerbi, A. and D. Tasche
Page 419: Malevergne, Y. and D. Sornette, 200
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Page 425 and 426: Multi-Moments Method for Portfolio
Page 427 and 428: choosen risk measure. Section 5 pre
Page 429 and 430: The variance of the return X of an
Page 431 and 432: This property is verified for all c
Page 433 and 434: µn=α of order n = 2, 4, 6 and 8.
Page 435 and 436: these two assets or portfolios. The
Page 437 and 438: Due to the homogeneity property of
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Page 441 and 442: C. Then, if g1(X1), · · · , gn(X
Page 443 and 444: Differentiating with respect to x1,
Page 445 and 446: 7.2 Transformation of the modified
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Page 449 and 450: 8.3 Non-symmetric assets In the cas
Page 451 and 452: y the variance will then increase).
Page 453 and 454: A Description of the data set We ha
Page 455 and 456: thus and finally 1 λ1 n−1 = w
Page 457 and 458: C Composition of the market portfol
Page 459 and 460: D Generalized capital asset princin
Page 461 and 462: This brings us back to the problem
Page 463 and 464: F.2 General case We now consider a
Page 465 and 466: Harvey, C.R. and A. Siddique, 2000,
Page 467 and 468: µ µ2 1/2 µ4 1/4 µ6 1/6 µ8 1/8
Page 469 and 470: 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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