Utility functions, risk aversion, preference switching, portfolio selection probem
This paper deals with switched utility functions. The usual classification of utility functions is based on the signs of its derivatives representing a risk attitude of a decision maker. This approach leads to a stochastic dominance criteria for decision making. Especially, the positive second derivative of a utility function is a very common assumption and it corresponds to risk averse investors and second-order stochastic dominance relation. The switched utility functions present the alternative way to utility function characterisations. While stochastic dominance approach compare two given random variables (gambles) for all considered utility functions, switched utility functions analyze a given utility function for all considered gambles. This analysis is based on the number of switching preferences between two gambles due to changes in initial wealth. If we consider a portfolio selection problem as a maximizing expected utility problem, another approach to utility function characterizations can prefer the utility functions making this problem computationally less demanding. Especially, linear, piecewise linear and quadratic utility functions allow us to solve portfolio selection problem as a linear or quadratic programming problem. The aim of this paper is to compare these three ways of utility function classifications, mainly to analyze the switched properties of computationally attractive utility functions.