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 publication extends conventional ways of probability size and portfolio optimization via combining distributional versions with possibility or functionality measures into one framework. all through those pages, the specialist authors clarify the basics of chance metrics, define new techniques to portfolio optimization, and speak about various crucial possibility measures. utilizing quite a few examples, they illustrate more than a few functions to optimum portfolio selection and hazard conception, in addition to purposes to the realm of computational finance that could be important 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
Example text
P(Yn ≤ yn )) = C(FY1 (y1 ), . . , FYn (yn )), where FYi (yi ), i = 1, . . , n denote the marginal distribution functions of the random variables Y i , i = 1, . . , n. 19 Mikosch ¨ (2006), Embrechts and Puccetti (2006), and Ruschendorf (2004) provide examples and further references for the application of copulas in risk management. 20 The importance of copulas in the modeling of the distribution of multivariate random variables is provided by Sklar’s theorem. The derivation was provided in Sklar (1959).
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 . It turns out that all points of local extrema of the objective function are characterized by a zero gradient. As a result, the points yielding the local extrema of the objective function are among the solutions of the system of equations, ∂f (x) =0 ∂x1 ... ∂f (x) = 0. 3) is often referred to as representing the first-order condition for the objective function extrema.
There is a connection between minimization and maximization. Maximizing the objective function is the same as minimizing the negative of the objective function and then changing the sign of the minimal value, maxn f (x) = − minn [−f (x)]. 1. As a consequence, problems for maximization can be stated in terms of function minimization and vice versa. 1 Minima and Maxima of a Differentiable Function If the second derivatives of the objective function exist, then its local maxima and minima, often called generically local extrema, can be characterized.
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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