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 e-book extends conventional techniques of danger size and portfolio optimization by means of combining distributional types with hazard or functionality measures into one framework. all through those pages, the professional authors clarify the basics of likelihood metrics, define new techniques to portfolio optimization, and talk about a number of crucial threat measures. utilizing a variety of examples, they illustrate a number of functions to optimum portfolio selection and threat concept, in addition to purposes to the realm of computational finance that could be valuable to monetary engineers.

**Read or Download Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures PDF**

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**Additional info for Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures**

**Sample text**

In this discussion, we consider only the copulas with a density. 7 The copula density of a two-dimensional normal distribution. 8. 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.

18 ADVANCED STOCHASTIC MODELS (univariate distribution) to that of multiple random variables (multivariate distribution). , multiple random variables). For example, the theory of efficient portfolios covered in Chapter 8 assumes that returns of alternative investments have a joint multivariate distribution. 1 Conditional Probability A useful concept in understanding the relationship between multiple random variables is that of conditional probability. Consider the returns on the stocks of two companies in one and the same industry.

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. Working paper, London School of Economics. ¨ Ruschendorf, L. (2004). ‘‘Comparison of multivariate risks and positive dependence,’’ Journal of Applied Probability 41(2): 391–406.

### 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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