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## CAPM-Like Model and the Special Form of the Utility Function

The variance and semivariance are traditional measures of asset returns volatility since Markowitz proposed the market portfolio theory. Well known models for expected asset returns were developed under assumptions of mean-variance or mean-semivariance investor’s behavior. But numerous papers provided arguments against these models because of unrealistic assumptions and controversial empiric evidence. More complicated models with downside risk measures experienced difficulties with applications. The new model based on the special form of the investor’s utility function is proposed in this paper.

This paper contains the research of neuroeconomics results such as formulation and analysis of Ultimatum game (see Alan G. Sanfey, 2003) and neuromarketing (see Patrick Renvoisé, 2005). As a result the rational behavior of consumer during the decision-making of consume object prejudiced. In particular the axiom of reflexiveness of the rational utility theory was disproved. That axiom maintains that the fixed set of goods is not worse that itself. A conclusion that consumer choice based on the utility criterion depends not only on the set of goods but on the consume environment was made. The hypothesis of irrational behavior allowed to formalize floating utility criterion and correlation between the basket of products utility and consume environment during the consumer decision-making. Based on floating utility criterion the problem of optimal consumer’s budget distribution in conditions of integral utility maximization on limited time interval and consideration of the predicted environment factors value posed. Then the problem of intertemporal consumer choise for floating criterion was posed. The solution analysis of that problems had allowed to draw a conclusion of a significant influence of the predicted environment factors value exactness on an optimal solution and a dependence of that exactness on a consumer satisfaction.

We develop a model of asset pricing and hedging for interconnected financial markets with frictions – transaction costs and portfolio constraints. The model is based on a control theory for random fields on a directed graph. Market dynamics are described by using von Neumann – Gale dynamical systems first considered in connection with the modelling of economic growth [13,24]. The main results are hedging criteria stated in terms of risk-acceptable portfolios and consistent price systems, extending the classical superreplication criteria formulated in terms of equivalent martingale measures.

The paper suggests a new --- to the best of the author's knowledge --- characterization of Pareto-optimal decisions for the case of two-dimensional utility space which is not supposed to be convex. The main idea is to use the angle distances between the bisector of the first quadrant and points of utility space. A necessary and sufficient condition for Pareto optimality in the form of an equation is derived. The first-order necessary condition for optimality in the form of a pair of equations is also obtained.

Overvaluation on financial markets, high price volatility and quite rapid reduction of emerging markets towards an investment behavior field in terms of predictive estimation and forecast of further market changes. Hereby decision-making basis is a personal investment understanding and, due to favorable business climate, could build up the growth of irrational exuberance and speculative bubbles on financial markets.

This study models Market Certainty Index as a measure of asset overpricing and market overvaluation in terms of a speculative bubble concept. The results also provide insights of how to enhance the facility of overpriced assets studies at non-transparent economies or emerging markets.

We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.

We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.

We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.