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Novosyolov A.A.
Some properties of the relative mean function.
Proceedings of the 9th International Scientific School "Modelling and Analysis of Safety and Risk in Complex Systems"
, St.-Petersburg, 2009, 75-80.
Abstract
Preferences on sets of risks are usually described by real functionals on the sets, or by direct setting a (partial) order, e.g. stochastic dominance, which is defined via distribution descriptors. One of examples of distribution descriptors in case of finite expectation is the relative mean function. The paper is devoted to studying some properties of the relative mean function and to establishing its relationship with stochastic dominance orders.
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Novosyolov A.A.
Stress testing in factor models of market risk.
Proceedings of the XI All-Russian conference "Problems of regional informaization", Krasnoyarsk, SibGTU, 2009, 199-201 (in Russian)
Abstract
A method of stress testing based on correlation increasing is considered in the paper. The method allows keeping positive definiteness of correlation matrices under all admissible distortions. It is shown that inreasing correlations leads to much greater increase in VaR than increasing factors volatility does.
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Novosyolov A.A.
Reproducing discrete distributions with predefined correlation structure.
Proceedings of the II scientific conference «Actual problems of contemporary science and their solution»
, Krasnoyarsk, EGTEI, 2009, 229-234. (in Russian)
Abstract
Reproducing multidimensional normal distribution with predefined correlation structure is a well known problem, and is usually done via factorization of covariance matrix. The method does not work for discrete distributions. In the paper we describe a method of reconstructing two-dimensional discrete distribution by its marginals and correlation coefficient. The method is based on mixing some basic tw0-dimensional distributions on the lattice provided.
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Novosyolov A.A.
Discrete distributions with given correlation least deviated from independent joint distribution.
Proceedings of the XIII International conference on eventological mathematics and related topics
, Krasnoyarsk, KGTEI, SFU, 2009, 126-131. (in Russian)
Abstract
Obtaining a normal distribution with given correlation structure is a well studied problem, which is usually implemented via covariance matrix factorization. The method does not work for discrete distributions. In the present paper we describe a method of building a two-dimensional discrete distribution by its marginal distributions and correlation coefficient. The method is based on looking for a distribution least deviated from the independent distribution.
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Novosyolov A.A.
Representing distributions by mixtures of Bernoulli distributions.
Proceedings of the VIII International conference on financial and actuarial mathematics and related topics
, Krasnoyarsk, KGTEI, SFU, 2009, 179-183. (in Russian)
Abstract
Representing complicated distributions by mixtures of simple distributions is a useful tool for solving probability problems. In particular, representing any distribution with zero mean by a mixture of Bernoulli distributions with zero mean may be used in calculating risk aversion in various preference models. In the present paper we derive one such representation.
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