This paper studies the problem of optimal decision-making under uncertainty by an agent whose information processing abilities, required in particular for evaluation of expectations, are limited. Our approach is based on the apparatus of information theory and utilizes the techniques of the economic theory of rational inattention; however, the latter are used in a novel way — instead of restraining the external perception of agents, we are concerned with constraints on agents internal cognition. The resulting concept of expectations constrained by information processing capacity nests rational expectations as a special case. Preliminary results of its application to the problem of optimal portfolio choice are quite encouraging. For example, we obtained an intriguing new insight into the 'equity premium puzzle': there should be a 'perceived' high premium on risky assets due to the very fact that outside observers ('econometricians') devote less information processing capacity to evaluating expected returns on risky assets than inside actors ('market participants') do.