By Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi CFA
This groundbreaking ebook extends conventional ways of chance dimension 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 methods to portfolio optimization, and speak about various crucial danger measures. utilizing various examples, they illustrate various purposes to optimum portfolio selection and danger thought, in addition to functions to the realm 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 (Frank J. Fabozzi Series)
Y ≤ −10%? Essentially, the conditional probability is calculating the probability of an event provided that another event happens. If we denote the first event by A and the second event by B, then the conditional probability of A provided that B happens, denoted by P(A|B), is given by the formula, P(A|B) = P(A ∩ B) , P(B) which is also known as the Bayes formula. According to the formula, we divide the probability that both events A and B occur simultaneously, denoted by A ∩ B, by the probability of the event B.
5) can be used to estimate the probability of observing a large observation by means of the mathematical expectation and the level . Chebyshev’s inequality is rough as demonstrated geometrically in the following way. 9 Chebyshev’s inequality, a geometric illustration. The area of the rectangle in the upper-left corner is smaller than the shaded area. which means that it equals the area closed between the distribution function and the upper limit of the distribution function. 9 as the shaded area above the distribution function.
Kluppelberg and T. Mikosch (1997). Modeling extremal events for insurance and finance, Springer. , 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.
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