In this paper we consider a new class of dynamic pricing principles and
recursive utilities. We start with the interpretation of the generator of a
backward stochastic differential equation as an infinitesimal pricing rule or
an instantaneous utility. With this interpretation the generator has an
economic meaning and describes the subjective views of the investor concerning
the expected change in the price or the utility. We give a motivation for
considering non-Markovian generators of BSDEs which leads us to the study of
so-called time-delayed backward stochastic differential equations. We
investigate two pricing principles and recursive utilities which are derived
from time-delayed BSDEs with generators of a moving average type. They might be
useful in the case of an individual valuation of a pay-off. A non-Markovian
generator arises when the local valuation rule of the investor depends on the
past values of prices, volatilities or utilities. Some properties of our new
pricing principles and recursive utilities are considered and we show that they
are fundamentally different from the properties which hold for prices and
utilities based on classical BSDEs. An interpretation of this fact is provided.