UDC 519.53

A.V. Starikov, M.L. Lapshina, S.V. Pisareva, A.A. Gribanov, A.L. Boykova

The paper describes a class of utility functions whose derivative is representable as a Laplace transform. The basic properties for the utility functions belonging to the described class are formulated. The problem of stochastic domination is analyzed, limiting properties of indices of absolute and relative risk aversion are investigated. The expediency of separating the utility function from the whole set is due to two considerations. First, this class includes almost all traditionally used in describing investors behavior of the utility function. Secondly, each function in L can be represented approximately as a sum with positive coefficients of exponential phase transitions. The main focus of the work is on two analytical methods. The first is the task of strengthening and mitigating risks, when a risk-averse investor has to decide what is best: to expose your income to participation in two risky projects, or to give up risk altogether, or to participate only in one of the projects? The second aspect highlights the behavior of absolute and relative risk aversion indicators. In this paper we give a more complete integral representation of functions belonging to L, and, a systematic description of the class; the statement is formulated in terms of lottery preference, fully characterizing the class, the basic mathematical concepts and properties of completely monotonic functions that are necessary for formal description and study of the introduced class, the precise definition of the class of the utility function, the characteristics of the basic properties and the statement of necessary and sufficient conditions for the function usefulness of the class being studied. In the article the question of stochastic domination on the introduced class is considered, corresponding criteria of domination are given. The findings are used further in connection with the task of strengthening or mitigating the risk with the simultaneous impact of independent random factors on the income of the investor. Finally, the paper presents an analysis of the asymptotic properties of the absolute and relative risk aversion indicators for utility functions from the introduced class

Keywords: utility function, class, risk, alternative, securities, preferences.

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