  We show in a simulation when economic agents are subject to evolution (random
change and selection based on the success in the estimation of the result of
the gamble) they acquire risk aversive behavior. This behavior appears in the
form of adjustment of their estimation of probabilities when calculating the
expected value (ensemble average). It means that their subjective probabilities
evolve in such a way that economic agents tend to assign lower probabilities to
"good" events and higher probabilities to "bad" events. These subjective
probabilities can be derived analytically by assuming that economic agents care
about time average, not the ensemble average. Probabilities calculated based on
this assumption are equal to the probabilities we get in evolutionary
simulation. Furthermore, it appears that these subjective probabilities are
equal to risk-neutral probabilities in mathematical finance. Hence, by taking
into account that the environment in which economic agents operate is
non-ergodic, we are able to calculate risk-neutral probabilities that are
consistent with modern finance theory but are derived in a conceptually
different way. It means that when we assume that agents try to predict time
average, not ensemble average, the need for the concept of risk aversion
disappears, since there is no distortion of subjective probabilities.
Evolutionary simulations are quite a general method that can be applied for the
determination of relevant measures of the outcome of a gamble under various
conditions.
