  A classical portfolio theory deals with finding the optimal proportion in
which an agent invests a wealth in a risk-free asset and a probabilistic risky
asset. Formulating and solving the problem depend on how the risk is
represented and how, combined with the utility function defines a notion of
expected utility. In this paper the risk is a fuzzy variable and the notion of
expected utility is defined in the setting of Liu's credibility theory. Thus
the portfolio choice problem is formulated as an optimization problem in which
the objective function is a credibilistic expected utility. Different
approximation calculation formulas for the optimal allocation of the
credibilistic risky asset are proved. These formulas contain two types of
parameters: various credibilistic moments associated with fuzzy variables
(expected value, variance, skewness and kurtosis) and the risk aversion,
prudence and temperance indicators of the utility function.
