Abstract:
The work investigates theoretical and qualitative properties of parametric families of risk-preference functions (r. p. f.) of an investor, who upholds the continuous VaR-criterion (CC-VaR). The investor in problems with such a criterion selects not family but only one function. Nevertheless, the knowledge of families' properties has to help the investor to better formalize risk preferences. The conception of families' correctness that is connected with their yield and important for applying CC-VaR is introduced. One-parametric families are correct, if their yields are monotone functions of the parameter at arbitrary possible answer of the market. The families' analysis is prosecuted on base of normalized r. p. f., for which the integral in its domain is independent of parameter. The theorem about necessary and sufficient condition of families' correctness with some useful consequences is formulated and proved. An example of two-parametric superfamily of linear r. p. f. with one fracture that generates one-parametric correct families with special property of symmetry is considered. The example substantiates the hypothesis of quality type that more «profitable» r. p. f. as compared with a rival one generates lower incomes near zero and higher incomes near one. Analytical investigations are accompanied by computations and diagrams.
Keywords:continuous VaR-criterion (CC-VaR), risk preferences function, families of risk preferences functions, income, investment amount, yield, correct and incorrect families.
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