56 results found
Anoshkina V, Davidova Z, Ibragimov M, et al., 2009, Labor market equilibrium and income tax rates: The case of Uzbekistan, Tax Policy and Practice (Moscow, Russia)
Ibragimov R, 2009, Portfolio diversification and value at risk under thick-tailedness, Quantitative Finance, Vol: 9, Pages: 565-580, ISSN: 1469-7688
This paper focuses on the study of portfolio diversification and value at risk analysis under heavy-tailedness. We use a notion of diversification based on majorization theory that will be explained in the text. The paper shows that the stylized fact that portfolio diversification is preferable is reversed for extremely heavy-tailed risks or returns. However, the stylized facts on diversification are robust to heavy-tailedness of risks or returns as long as their distributions are moderately heavy-tailed. Extensions of the results to the case of dependence, including convolutions of α-symmetric distributions and models with common shocks are provided.
Ibragimov R, 2009, Heavy-tailed densities, THE NEW PALGRAVE DICTIONARY OF ECONOMICS ONLINE, Editors: Durlauf, Blume, Publisher: Palgrave Macmillan
Ibragimov R, 2008, Heavy-tailedness and threshold sex determination, STATISTICS & PROBABILITY LETTERS, Vol: 78, Pages: 2804-2810, ISSN: 0167-7152
Ibragimov R, 2008, A tale of two tails: peakedness properties in inheritance models of evolutionary theory, JOURNAL OF EVOLUTIONARY ECONOMICS, Vol: 18, Pages: 597-613, ISSN: 0936-9937
Ibragimov R, Phillips PCB, 2008, Regression asymptotics using martingale convergence methods, ECONOMETRIC THEORY, Vol: 28, Pages: 1-60
Ibragimov R, Walden J, 2008, Portfolio diversification under local and moderate deviations from power laws, Insurance: Mathematics and Economics, Vol: 42, Pages: 594-599, ISSN: 0167-6687
This paper analyzes portfolio diversification for nonlinear transformations of heavy-tailed risks. It is shown that diversification of a portfolio of convex functions of heavy-tailed risks increases the portfolio’s riskiness if expectations of these risks are infinite. In contrast, for concave functions of heavy-tailed risks with finite expectations, the stylized fact that diversification is preferable continues to hold. The framework of transformations of heavy-tailed risks includes many models with Pareto-type distributions that exhibit local or moderate deviations from power tails in the form of additional slowly varying or exponential factors. The class of distributions under study is therefore extended beyond the stable class.
Ibragimov M, Ibragimov R, 2008, Optimal constants in the Rosenthal inequality for random variables with zero odd moments, Statistics and Probability Letters, Vol: 78, Pages: 186-189, ISSN: 0167-7152
We obtain estimates for the best constant in the Rosenthal inequality for independent random variables with zero first odd moments, . The estimates are sharp in the extremal cases and , that is, in the cases of random variables with zero mean and random variables with zero first odd moments.
Ibragimov M, Ibragimov R, 2007, Market demand elasticity and income inequality, ECONOMIC THEORY, Vol: 32, Pages: 579-587, ISSN: 0938-2259
Ibragimov R, Walden J, 2007, The limits of diversification when losses may be large, Journal of Banking and Finance, Vol: 31, Pages: 2551-2569, ISSN: 1872-6372
Recent results in value at risk analysis show that, for extremely heavy-tailed risks with unbounded distribution support, diversification may increase value at risk, and that generally it is difficult to construct an appropriate risk measure for such distributions. We further analyze the limitations of diversification for heavy-tailed risks. We provide additional insight in two ways. First, we show that similar non-diversification results are valid for a large class of risks with bounded support, as long as the risks are concentrated on a sufficiently large interval. The required length of the support depends on the number of risks available and on the degree of heavy-tailedness. Second, we relate the value at risk approach to more general risk frameworks. We argue that in markets for risky assets where the number of assets is limited compared with the (bounded) distribution support of the risks, unbounded heavy-tailed risks may provide a reasonable approximation. We suggest that this type of analysis may have a role in explaining various types of market failures in markets for assets with possibly large negative outcomes.
Ibragimov R, 2007, Efficiency of linear estimators under heavy-tailedness: Convolutions of α-symmetric distributions, Econometric Theory, Vol: 23, Pages: 501-517, ISSN: 0266-4666
This paper focuses on the analysis of efficiency, peakedness, and majorization properties of linear estimators under heavy-tailedness assumptions. We demonstrate that peakedness and majorization properties of log-concavely distributed random samples continue to hold for convolutions of α-symmetric distributions with α > 1. However, these properties are reversed in the case of convolutions of α-symmetric distributions with α < 1.We show that the sample mean is the best linear unbiased estimator of the population mean for not extremely heavy-tailed populations in the sense of its peakedness. In such a case, the sample mean exhibits monotone consistency, and an increase in the sample size always improves its performance. However, efficiency of the sample mean in the sense of peakedness decreases with the sample size if it is used to estimate the location parameter under extreme heavy-tailedness. We also present applications of the results in the study of concentration inequalities for linear estimators.
Ibragimov R, 2007, Thou shalt not diversify: Why 'two of every sort'?, JOURNAL OF APPLIED PROBABILITY, Vol: 44, Pages: 58-70, ISSN: 0021-9002
de la Pena VH, Ibragimov R, Sharakhmetov S, 2006, Characterizations of joint distributions, copulas, information, dependence and decoupling, with applications to time series, 2ND ERICH L. LEHMANN SYMPSIUM - OPTIMALITY, Editors: Rojo, Pages: 183-209
Ibragimov R, 2005, New Majorization Theory in Economics and Martingale Convergence Results in Econometrics
Ibragimov R, 2004, Option bounds, JOURNAL OF APPLIED PROBABILITY, Vol: 41A, Pages: 145-156
Ibragimov R, 2003, On extremal distributions and sharp Lp-bounds for sums of multilinear forms, Annals of Probability, Vol: 31, Pages: 630-675
de la Pena VH, Ibragimov R, Sharakhmetov S, 2002, On sharp Burkholder-Rosenthal-type inequalities for infinite-degree U-statistics, ANNALES DE L'INSTITUTE H. POINCARE - PROBABILITES ET STATISTIQUES, Vol: 38, Pages: 973-990
Ibragimov R, Sharakhmetov S, 2002, Bounds on moments of symmetric statistics, STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, Vol: 39, Pages: 251-275
Ibragimov R, Sharakhmetov S, 2002, A characterization of joint distribution of two-valued random variables and its applications, JOURNAL OF MULTIVARIATE ANALYSIS, Vol: 83, Pages: 389-408
Ibragimov R, Sharakhmetov S, 2002, The exact constant in the Rosenthal inequality for random variables with mean zero, THEORY OF PROBABILITY AND ITS APPLICATIONS, Vol: 46, Pages: 127-131
Ibragimov R, Sharakhmetov S, 2001, The best constant in the Rosenthal inequality for nonnegative random variables, STATISTICS & PROBABILITY LETTERS, Vol: 55, Pages: 367-376, ISSN: 0167-7152
Ibragimov R, Sharakhmetov S, Cecen A, 2001, Exact estimates for moments of random bilinear forms, JOURNAL OF THEORETICAL PROBABILITY, Pages: 21-37
Ibragimov R, Sharakhmetov S, 1999, Analogues of Khintchine, Marcinkiewicz-Zygmund and Rosenthal Inequalities for Symmetric Statistics, SCANDINAVIAN JOURNAL OF STATISTICS, Vol: 26, Pages: 621-633, ISSN: 0303-6898
Ibragimov R, Sharakhmetov S, 1998, On an Exact Constant for the Rosenthal Inequality, THEORY OF PROBABILITY & ITS APPLICATIONS, Vol: 42, Pages: 294-302, ISSN: 0040-585X
Ibragimov R, 1997, Estimates for moments of symmetric statistics
Ibragimov R, 2009, Heavy-tailed densities, The New Palgrave Dictionary of Economics Online, Publisher: Palgrave Macmillan
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