# Svetlozar T. Rachev, Stoyan V. Stoyanov, Visit Amazon's's Advanced Stochastic Models, Risk Assessment, and Portfolio PDF

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 methods of chance size and portfolio optimization through combining distributional types with threat or functionality measures into one framework. all through those pages, the professional authors clarify the basics of chance metrics, define new ways to portfolio optimization, and speak about a number of crucial hazard measures. utilizing a number of examples, they illustrate more than a few functions to optimum portfolio selection and hazard concept, in addition to purposes to the realm of computational finance that could be precious 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 resources for Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures**

**Example text**

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. In a similar way, the upper Fr´echet bound, sometimes referred to as the maximal copula, represents perfect positive dependence between the two random variables. 8 SUMMARY We considered a number of concepts from probability theory that will be used in later chapters in this book.

38 ADVANCED STOCHASTIC MODELS Denote by ∇f (x) the vector of the first partial derivatives of the objective function evaluated at x, ∇f (x) = ∂f (x) ∂f (x) . , ∂x1 ∂xn This vector is called the function gradient. At each point x of the domain of the function, it shows the direction of greatest rate of increase of the function in a small neighborhood of x. If for a given x, the gradient equals a vector of zeros, ∇f (x) = (0, . . , 0) then the function does not change in a small neighborhood of x ∈ Rn .

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. In a similar way, the upper Fr´echet bound, sometimes referred to as the maximal copula, represents perfect positive dependence between the two random variables.

### 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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