Advanced Stochastic Models, Risk Assessment, and Portfolio by Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi

By Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi CFA

This groundbreaking booklet extends conventional techniques of chance size and portfolio optimization through combining distributional versions with threat or functionality measures into one framework. all through those pages, the professional authors clarify the basics of chance metrics, define new ways to portfolio optimization, and talk about quite a few crucial threat measures. utilizing various examples, they illustrate a variety of purposes to optimum portfolio selection and possibility concept, in addition to purposes to the realm of computational finance which may be worthy 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 (Frank J. Fabozzi Series)

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General types of dispersion measures are discussed in Chapter 6. 3 Asymmetry A probability distribution may be symmetric or asymmetric around its mean. A popular measure for the asymmetry of a distribution is called its skewness. 4 The density graphs of a positively and a negatively skewed distribution. 4). 4). 4 Concentration in Tails Additional information about a probability distribution function is provided by measuring the concentration (mass) of potential outcomes in its tails. The tails of a probability distribution function contain the extreme values.

This analysis indicates that the copula density function provides information about the local dependence structure of a multidimensional random 30 ADVANCED STOCHASTIC MODELS variable Y relative to the case of stochastic independence. 8 provides an illustration is the two-dimensional case. 6. All points that have an elevation above 1 have a local dependence implying that the events Y 1 ∈ (y1 , y1 + ) and Y 2 ∈ (y2 , y2 + ) for a small > 0 are likely to occur jointly. This means that in a large sample of observations, we observe the two events happening together more often than implied by the independence assumption.

2) and, therefore, the argument for which f 0 is achieved may not be unique. 2) holds, then the function is said to attain its global minimum at x0 . 2) holds for x belonging only to a small neighborhood of x0 and not to the entire space Rn , then the objective function is said to have a local minimum at x0 . 1 The relationship between minimization and maximization for a one-dimensional function. for all x such that ||x − x0 ||2 < where ||x − x0 ||2 stands for the Euclidean distance between the vectors x and x0 , n x − x0 2 = (xi − x0i )2 , i=1 and is some positive number.

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