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464 14. Gestion de Portefeuilles multimoments et équilibre de marché References Acerbi, C., 2002, Spectrale measures of risk : a coherent representation of subjective risk aversion, Journal of Banking and Finance. Alexander, G.J. and A.M. Baptista, 2002, Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis, Journal of Economic Dynamics and Control 26, 1159-1193. Abramovitz, E. and I.A. Stegun, 1972, Handbook of Mathematical functions (Dover Publications, New York). Allais, M., 1953, Le comportement de l’homme rationel devant le risque, critique des postulat de l’école américaine, Econometrica 21, 503-546. Allais, M., 1990, Allais Paradox, in The new palgrave, Utility and probability, Macmillan, 3-9. Andersen, J.V., and D. Sornette, 2001, Have your cake and eat it too: increasing returns while lowering large risks! Journal of Risk Finance 2, 70-82. Artzner, P., F. Delbaen, J.M. Eber and D. Heath, 1997, Thinking coherently, Risk 10, 68-71. Artzner, P., F. Delbaen, J.M. Eber and D. Heath, 1999, Coherent measures of risk, Math. Finance 9, 203-228. Bouchaud, J.-P., D. Sornette, C. Walter and J.-P. Aguilar, 1998, Taming large events: Optimal portfolio theory for strongly fluctuating assets, International Journal of Theoretical and Applied Finance 1, 25-41. Dowd, K., 2000, Adjusting for risk: an improved Sharpe ratio, International Review of Economics and Finance 9, 209-222. Embrechts, P., C. Kluppelberg and T. Mikosh, 1997, Modelling extremal events (Springel-Verlag, Applications of Mathematics 33). Embrecht, P., A. McNeil and D. Straumann, 1998, Correlation and Dependence in risk management: properties and pitfalls, Proceedings of the Risk Management workshop at the Newton Institute Cambridge, Cambridge University Press. Fang, H. and T. Lai, 1997, Co-kurtosis and capital asset pricing, Financial Review 32, 293-307. Föllmer, H. and A. Schied, 2002, Convex measures of risk and trading constraints, Finance and Stochastics 6, forthcoming. Föllmer, H. and A. Schied, 2002, Robust preferences and convex measures of risk, Working paper. Frisch, U. and D. Sornette, 1997, Extreme Deviations and Applications, J. Phys. I France 7, 1155-1171. 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., J.P. Laurent and O. Scaillet, 2000, Sensitivity analysis of Values at Risk, Journal of Empirical Finance 7,225-245. Gradshteyn, I.S. and I. M. Ryzhik, 1965, Table of integrals Series and Products, Academic Press. 40
Harvey, C.R. and A. Siddique, 2000, Conditional skewness in asset pricing tests, Journal of Finance 55, 1263-1295. Hill, B.M., 1975, A Simple General Approach to Inference about the Tail of a Distribution, Annals of statistics, 3(5), 1163-1174. Hwang, S. and S. Satchell, 1999, Modelling emerging market risk premia using higher moments, International Journal of Finance and Economics 4, 271-296. Jorion, P., 1997, Value-at-Risk: The New Benchmark for Controlling Derivatives Risk (Irwin Publishing, Chicago, IL). Jurcenko, E. and B. Maillet, 2002, The four-moment capital asset pricing model: some basic results, Working Paper. Karlen, D., 1998, Using projection and correlation to approximate probability distributions, Computer in Physics 12, 380-384. Krauss, A. and R. Litzenberger, 1976, Skewness preference and the valuation of risk assets, Journal of Finance 31, 1085-1099. 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. Lim, K.G., 1989, A new test for the three-moment capital asset pricing model, Journal of Financial and Quantitative Analysis 24, 205-216. Lindskog, F., 2000, Modelling Dependence with Copulas, http : //www.risklab.ch/P apers.html#MT Lindskog Lintner, J. 1975, The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics 13, 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. and D. Sornette, 2001, Testing the Gaussian copula hypothesis for financial assets dependences. http : //papers.ssrn.com/sol3/papers.cfm?abstract id = 291140 Markovitz, H., 1959, Portfolio selection : Efficient diversification of investments (John Wiley and Sons, New York). Merton, R.C., 1990, Continuous-time finance, (Blackwell, Cambridge). Mossin, J., 1966, Equilibrium in a capital market, Econometrica 34, 768-783. Muzy, J.-F., D. Sornette, J. Delour and A. Arneodo, 2001, Multifractal returns and Hierarchical Portfolio Theory, Quantitative Finance 1 (1), 131-148. Nelsen, R.B. 1998, An Introduction to Copulas. Lectures Notes in statistic, 139, Springer Verlag, New York. Pagan, A., 1996, The Econometrics of Financial Markets, Journal of Empirical Finance, 3, 15 - 102. 41 465
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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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11.5. Annexe 369 Collective Origin
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11.5. Annexe 371 point λ = 1. Thus
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Chapitre 12 Gestion des risques gra
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12.1. Comprendre et gérer les risq
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12.2. Minimiser l’impact des gran
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Chapitre 13 Gestion de portefeuille
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VaR-Efficient Portfolios for a Clas
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dependence: from independence to co
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given a series of return {rt}t foll
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eads cV (u1, · · · , un) = 1
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THEOREM 4 (TAIL EQUIVALENCE FOR A S
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Independent Assets Comonotonic Asse
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3.2 Typical recurrence time of larg
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and finally w ∗ i = χ−1 i j
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where the ˆwi’s are solution of
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Choosing x > y > Aɛ, and applying
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Expanding fi(xi) around x ∗ i yie
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for all h ∈ AC. Thus, integrating
Page 413 and 414: B Asymptotic distribution of the su
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Page 417 and 418: References Acerbi, A. and D. Tasche
Page 419 and 420: Malevergne, Y. and D. Sornette, 200
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
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: F.2 General case We now consider a
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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Page 473 and 474: w i w i 0.2 0.15 0.1 0.05 Mean−μ
Page 475 and 476: Figure 6: Schematic representation
Page 477 and 478: Empirical Cumulative Distribution 1
Page 479 and 480: Z 2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0
Page 481 and 482: Z 2 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0
Page 483 and 484: 10 0 10 −1 10 0 10 −1 10 −1 1
Page 485 and 486: 10 0 10 −1 10 0 10 −1 10 −1 1
Page 487 and 488: κ 22 20 18 16 14 12 10 8 6 4 2 Exc
Page 489 and 490: Return μ 0.12 0.11 0.1 0.09 0.08 0
Page 491 and 492: Conclusions et Perspectives L’obj
Page 493 and 494: Conclusion 493 en univers gaussien
Page 495 and 496: Annexe A Evaluation de la conduite
Page 497 and 498: A.2. Eléments de contexte 497 bora
Page 499 and 500: A.4. Compétences acquises et ensei
Page 501 and 502: A.5. Conclusion 501 de la recherche
Page 503 and 504: Bibliographie ACERBI, C. (2002) :
Page 505 and 506: Bibliographie 505 BOUCHAUD, J. P. E
Page 507 and 508: Bibliographie 507 DE FINETTI, B. (1
Page 509 and 510: Bibliographie 509 GRANGER, C. W. ET
Page 511 and 512: Bibliographie 511 LILLO, F. ET R. N
Page 513 and 514: Bibliographie 513 PATTON, A. (2001)
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Bibliographie 515 SUSMEL, R. (1996)
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