By Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi CFA
This groundbreaking publication extends conventional methods of hazard dimension and portfolio optimization by means of combining distributional versions with hazard 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 talk about various crucial hazard measures. utilizing various examples, they illustrate a variety of functions to optimum portfolio selection and possibility conception, in addition to purposes to the world of computational finance that could be important to monetary engineers.
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Extra info for Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures (Frank J. Fabozzi Series)
For example, the definite integral can be viewed as a functional because it assigns a real number to a function—the corresponding area below the function graph. A risk measure can also be viewed as a functional because it assigns a number to a random variable. Any random variable is mathematically described as a certain function the domain of which is the set of outcomes . Chapter 1 provides more details on the theory of probability. 42 ADVANCED STOCHASTIC MODELS satisfies the property: For a given α∈[0,1] and all x1 ∈ Rn and x2 ∈ Rn in the function domain, f (αx1 + (1 − α)x2 ) ≥ αf (x1 ) + (1 − α)f (x2 ).
The class of extreme value distributions forms a location-scale family. 6 Generalized Extreme Value Distribution Besides the previously mentioned (Gumbel type) extreme value distribution, there are two other types of distributions that can occur as the limiting distribution of appropriately standardized sample maxima. One class is denoted as the Weibull-type extreme value distribution and has a similar representation as the Weibull distribution. The third type is also referred to as the Fr´echet-type extreme value distribution.
Therefore, this case corresponds to these events being almost disjoint; that is, with a very small probability of occurring simultaneously. 4) is much larger than the denominator and, as a result, the copula density is larger than 1. In this case, fY (y1 , . . , yn ) > fY1 (y1 ) . . fYn (yn ), which means that the joint probability of the events that Y i is in a small neighborhood of yi for i = 1, 2, . . , n is larger than what it would if the corresponding events were independent. Therefore, copula density values larger than 1 mean that the corresponding events are more likely to happen simultaneously.
Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures (Frank J. Fabozzi Series) by Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi CFA