We first discuss about relationships between risk-sensitive control and robust utility maximization on a finite time horizon. We moreover show that analysis of the H-J-B equations of parabolic type gives us optimal strategies for the problems. Then we talk about large deviations approach to down-side risk minimization.  Analysis of the H-J-B equations of ergodic type relevant to risk-sensitive portfolio optimization leads to obtaining the estimates of the large deviations probability.