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By Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi CFA
This groundbreaking booklet extends conventional methods of probability size and portfolio optimization by way of combining distributional versions with possibility or functionality measures into one framework. all through those pages, the specialist authors clarify the basics of likelihood metrics, define new techniques to portfolio optimization, and talk about numerous crucial threat measures. utilizing quite a few examples, they illustrate quite a number functions to optimum portfolio selection and danger thought, in addition to purposes to the world of computational finance that could be worthwhile 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 (Frank J. Fabozzi Series)
I=1 the α-quantile for a continuous probability distribution P with strictly increasing cumulative distribution function F is obtained as qα = F−1 (α). 3 Calculation of Sample Moments. Moment Sample Moment r= Mean Variance s2 = Skewness ζˆ = Kurtosis κˆ = 1 k 1 k k ri i=1 k (ri − r)2 i=1 1 k k i = 1 (ri − (s2 )3/2 1 k k i = 1 (ri (s2 )2 r)3 − r)4 For large k, it is reasonable to expect that the average of the observations will not be far from the mean of the probability distribution. Now, we observe that all theoretical formulae for the calculation of the four statistical moments are expressed as means of something.
Furthermore, we also distinguish between types of optimization problems depending on the assumed properties of the objective function and the functions in the constraint set, such as linear problems, quadratic problems, and convex problems. The solution methods vary with respect to the particular optimization problem type as there are efficient algorithms prepared for particular problem types. In this chapter, we describe the basic types of optimization problems and remark on the methods for their solution.
And G. Puccetti (2006). ‘‘Bounds for functions of dependent risks,’’ Finance and Stochastics 10(3): 341–352. , S. -W. Ng (1994). Symmetric multivariate and related distributions, New York: Marcel Dekker. Johnson, N. , S. Kotz and A. W. Kemp (1993). , New York: John Wiley & Sons. Larsen, R. , and M. L. Marx (1986). An introduction to mathematical statistics and its applications, Englewed Clifs, NJ: Prentice Hall. Mikosch, T. (2006). ‘‘Copulas—tales and facts,’’ Extremes 9: 3–20. Patton, A. J. (2002).
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