Before revision:  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.
After revision:  We investigate two pricing principles and recursive utilities which are derived from time-delayed BSDEs with generators of a moving average type in the context of dynamic pricing 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.