The classical certainty equivalence theorem states that the optimal decision in a risky situation is the same as in some associated riskless situation. It holds true under rather specific conditions: quadratic payoff, linear relations between instruments and results.... When these conditions are not met but the various functions involved are differentiable, an approximate property can still be stated. The property is here proved and discussed for the following well known dynamic problem: when information accumulates over time how should one choose the sequence of values to be given to some instruments?