Download e-book for kindle: Advanced Stochastic Models, Risk Assessment, and Portfolio by Svetlozar T. Rachev, Stoyan V. Stoyanov, Visit Amazon's

By Svetlozar T. Rachev, Stoyan V. Stoyanov, Visit Amazon's Frank J. Fabozzi Page, search results, Learn about Author Central, Frank J. Fabozzi,

ISBN-10: 047005316X

ISBN-13: 9780470053164

ISBN-10: 0470253606

ISBN-13: 9780470253601

This groundbreaking ebook extends conventional techniques of chance size and portfolio optimization through combining distributional types with chance or functionality measures into one framework. all through those pages, the specialist authors clarify the basics of likelihood metrics, define new methods to portfolio optimization, and talk about various crucial threat measures. utilizing various examples, they illustrate quite a number purposes to optimum portfolio selection and chance idea, in addition to purposes to the world of computational finance that could be invaluable to monetary engineers.

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Extra resources for Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures

Sample text

6. 4) reveals that, if the random variable Y has independent components, then the density of the corresponding copula, denoted by c0 , is a constant in the unit hypercube, c0 (u1 , . . , un ) = 1 and the copula C0 has the following simple form, C0 (u1 , . . , un ) = u1 . . un . This copula characterizes stochastic independence. Now let us consider a density c of some copula C. 4) is a ratio of two positive quantities because the density function can only take nonnegative values. For each value of the vector of arguments y = (y1 , .

Ng (1994). Symmetric multivariate and related distributions, New York: Marcel Dekker. Johnson, N. , S. Kotz and A. W. Kemp (1993). , New York: John Wiley & Sons. Larsen, R. , and M. L. Marx (1986). An introduction to mathematical statistics and its applications, Englewed Clifs, NJ: Prentice Hall. Mikosch, T. (2006). ‘‘Copulas—tales and facts,’’ Extremes 9: 3–20. Patton, A. J. (2002). Application of copular theory in financial econometrics, Doctoral Dissertation, Economics, University of California, San Diego.

In this case, it has a simpler form because the marginal distributions are uniform. The lower and the upper Fr´echet bounds equal W(u1 , . . , un ) = max(u1 + · · · + un + 1 − n, 0) and M(u1 , . . , un ) = min(u1 , . . , un ) respectively. Fr´echet-Hoeffding inequality is given by W(u1 , . . , un ) ≤ C(u1 , . . , un ) ≤ M(u1 , . . , un ). In the two-dimensional case, the inequality reduces to max(u1 + u2 − 1, 0) ≤ C(u1 , u2 ) ≤ min(u1 , u2 ). In the two-dimensional case only, the lower Fr´echet bound, sometimes referred to as the minimal copula, represents perfect negative dependence between the two random variables.

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Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures by Svetlozar T. Rachev, Stoyan V. Stoyanov, Visit Amazon's Frank J. Fabozzi Page, search results, Learn about Author Central, Frank J. Fabozzi,


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