By Svetlozar T. Rachev, Stoyan V. Stoyanov, Visit Amazon's Frank J. Fabozzi Page, search results, Learn about Author Central, Frank J. Fabozzi,
This groundbreaking e-book extends conventional ways of danger dimension and portfolio optimization by way of combining distributional types with hazard or functionality measures into one framework. all through those pages, the specialist authors clarify the basics of chance metrics, define new methods to portfolio optimization, and speak about quite a few crucial possibility measures. utilizing a number of examples, they illustrate various functions to optimum portfolio selection and probability conception, in addition to functions to the world of computational finance that could be beneficial 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
2 Dispersion Another measure that can help us to describe a probability distribution function is the dispersion or how spread out the values of the random variable can realize. Various measures of dispersion are the range, variance, and mean absolute deviation. The most commonly used measure is the variance. It measures the dispersion of the values that the random variable can realize relative to the mean. It is the average of the squared deviations from the mean. The variance is in squared units.
On the plot, xα = αx1 + (1 − α)x2 1A function in mathematics can be viewed as a rule assigning to each element of a set D a single element of a set C. The set D is called the domain of f and the set C is called the codomain of f . A functional is a special kind of a function that takes other functions as its argument and returns numbers as output; that is, its domain is a set of functions. 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.
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 by Svetlozar T. Rachev, Stoyan V. Stoyanov, Visit Amazon's Frank J. Fabozzi Page, search results, Learn about Author Central, Frank J. Fabozzi,