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418 13. Gestion de portefeuille sous contraintes de capital économique Embrecht, P., A. Höing and A. Juri, 2002b, Using copulae to bound the Value-at-Risk for functions of dependent risks, Working Paper, Risklab. Fama, E.F., 1965, Portfolio analysis in a stable Paretian market, Management Science 11, 404-419. Fouque, J.-P., G. Papanicolaou, and R. Sircar, 2000, Derivatives in Financial Markets with Stochastic Volatility (Cambridge University Press, Cambridge, UK). Frisch, U. and D.Sornette, 1997, Extreme Deviations and Applications, Journal de. Physique I France 7, 1155-1171. Goldie, C. M. and C. Klüppelberg, 1998, Subexponential distributions, in A Practical Guide to Heavy Tails: Statistical Techniques and Applications, ed. R. L. Adler, R. Feldman, M. S. Taqqu, pp. 435-459 ( Birkhuser, Boston) Gopikrishnan, P., M. Meyer, L.A. Nunes Amaral and H.E. Stanley, 1998, Inverse cubic law for the distribution of stock price variations, European Physical Journal B 3, 139-140. Gouriéroux, C. and J. Jasiak, 1998, Truncated maximum likelyhood, goodness of fit tests and tail analysis, Working paper. Johansen, A. and D. Sornette, 1998, Stock market crashes are outliers, European Physical Journal B 1, 141-144. Johansen, A. and D. Sornette, 1998, Large market price drawdowns are outliers, Journal of Risk 4, 69-110. Jorion, P., 1997, Value-at-Risk: The New Benchmark for Controlling Derivatives Risk (Irwin Publishing, Chicago, IL). Kahneman, D. and A. Tversky, 1979, Prospect theort: An analysis of decision under risk, Econometrica 47, 263-291. Laherrère, J. and D. Sornette, 1998, Stretched exponential distributions in nature and economy : ”fat tails” with characteristic scales, European Physical Journal B 2, 525-539. Lintner, J., 1965, The valuation of risk assets and the selection of risky investments in stock portfolios and the capital bugets, Review of Economics and Statitics 41, 13–37. Litterman, R. and K. Winkelmann, 1998, Estimating covariance matrices (Risk Management Series, Goldman Sachs). Lux, T., 1996, The stable Paretian hypothesis and the frequency of large returns: an examination of major German stocks, Applied Financial Economics 6, 463-475. Malevergne, Y., V. Pisarenko and D. Sornette, 2002, Empirical distributions of log-returns: Exponential or power-like?, Working paper. Malevergne, Y. and D. Sornette, 2001, Testing the Gaussian copulas hypothesis for modeling financial assets dependence, Working paper, cond-mat/0111310. Malevergne, Y. and D. Sornette, 2002a, Minimising extremes, Risk 15(11), 129-133. Malevergne, Y. and D. Sornette, 2002b, How to account for extreme co-movements between individual stocks and the market, Working paper. 30
Malevergne, Y. and D. Sornette, 2002c, Multi-Moments Method for Portfolio Management: Generalized Capital Asset Pricing Model in Homogeneous and Heterogeneous markets, working paper http : //papers.ssrn.com/paper.taf?abstract id = 319544 Mantegna, R.N. and H.E. Stanley, 1995, Scaling bahavior of an economic index, Nature 376, 46-55. Markovitz, H., 1959, Portfolio selection : Efficient diversification of investments (John Wiley and Sons, New York). Mashal, R. and A. Zeevi, 2002, Beyond Correlation: Extreme Co-movements Between Financial Assets, Working paper, Columbia University, preprint at www.columbia.edu\ ∼rm586 Mossin, J., 1966, Equilibrium in capital asset market, Econometrica 35, 768–783. Nelsen, R.B., 1998, An Introduction to Copulas. Lectures Notes in statistic, 139 (Springer Verlag, New York). Rao, C.R., 1973, Linear statistical inference and its applications, 2d ed. (New York Willey). Rockafeller, R.T and S. Uryasev, 2000, Optimization of the conditional value-at-risk, journal of Risk 2, 21-41. Sharpe, W., 1964, Capital assets prices: a theory of market equilibrium under conditions of risk, Journal of Finance 19, 425–442. Sornette, D., 1998, Large deviations and portfolio optimization, Physica A 256, 251-283. Sornette, D., 2000, Critical Phenomena in Natural Sciences, Chaos, Fractals, Self-organization and Disorder: Concepts and Tools (Springer Series in Synergetics). Sornette, D., J. V. Andersen and P. Simonetti, 2000a, Portfolio Theory for “Fat Tails”, International Journal of Theoretical and Applied Finance 3, 523-535. Sornette, D., P. Simonetti, J.V. Andersen, 2000b, φ q -field theory for portfolio optimization : ”fat-tails” and non-linear correlations, Physics Reports 335, 19-92. Szergö, G., 1999, A critique to Basel regulation, or how to enhance (im)moral hazards, Proceedings of the International Conference on Risk Management and Regulation in Banking, Bank of Israel, Kluwer. Tasche, D. and L. Tilibetti, 2001, Approximations for the Value-at-Risk approach to risk-return, Working Paper. 31 419
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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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Page 369 and 370: 11.5. Annexe 369 Collective Origin
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Page 375 and 376: 12.1. Comprendre et gérer les risq
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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
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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
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Page 413 and 414: B Asymptotic distribution of the su
Page 415 and 416: This yields × h+ Sc−2 − 2 dh
Page 417: References Acerbi, A. and D. Tasche
Page 421 and 422: ln(T/T 0 ) T Figure 2: Logarithm
Page 423 and 424: Chapitre 14 Gestion de Portefeuille
Page 425 and 426: Multi-Moments Method for Portfolio
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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
Page 439 and 440: invested in the risky fund depends
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
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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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