Risk-sensitivity, large deviations and stochastic control

An exponential function of cost is adopted as a risk-sensitive criterion, and reasons given that this choice should be a natural one. It is shown that the analysis leads to risk-sensitive versions of the certainty-equivalence principle (separation principle) and of the maximum principle, and that these have a validity even outside the usual linear/quadratic/Gaussian framework. The methods are applied to some simple examples of economic interest.