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

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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 possibility dimension and portfolio optimization by way of combining distributional types with danger or functionality measures into one framework. all through those pages, the professional authors clarify the basics of chance metrics, define new techniques to portfolio optimization, and speak about numerous crucial probability measures. utilizing quite a few examples, they illustrate various functions to optimum portfolio selection and danger thought, in addition to purposes to the world of computational finance that could be helpful to monetary engineers.

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

Sample text

FYn (yn ). As a consequence, the joint probability of the events that Y i is in a small neighborhood of yi for i = 1, 2, . . , n is much smaller than what it would if the corresponding events were independent. 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, .

Xn ) . ∂x1 . . 2) Marginal Distributions Beside this joint distribution, we can consider the above mentioned marginal distributions, that is, the distribution of one single random variable Xi . 4 ∞ ∞ ... −∞ −∞ fX (x1 , . . , xi − 1 , x, xi + 1 , . . , xn )dx1 . . dxi − 1 dxi + 1 . . dxn Dependence of Random Variables Typically, when considering multivariate distributions, we are faced with inference between the distributions; that is, large values of one random variable imply large values of another random variable or small values of a third random variable.

In general, the distribution of Y might substantially differ from the distribution of X but in the case where X is normally distributed, the random variable Y is again normally distributed with parameters and µ˜ = aµ + b and σ˜ = aσ . Thus we do not leave the class of normal distributions if we multiply the random variable by a factor or shift the random variable. m. in degrees Celsius. Then Y = 95 X + 32 will give the temperature in degrees Fahrenheit, and if X is normally distributed, then Y will be too.

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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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