The maximum entropy principle can be used to assign utility values when only partial information is available about the decision makers preferences. In order to obtain such utility values it is necessary to establish an analogy between probability and utility through the notion of a utility density function. According to some authors [Soofi (1990), Abbas (2006a) (2006b), Sandow et al. (2006), Friedman and Sandow (2006), Darooneh (2006)] the maximum entropy utility solution embeds a large family of utility functions. In this paper we explore the maximum entropy principle to estimate the utility function of a risk averse decision maker.