SummaryWe introduce arisk‐sensitivegeneralization of the mixed control problem for linear stochastic systems with additive noise. Two criteria ofexponential‐quadraticform are used to generalise the usual quadratic criteria. The solutions are found in a linear state‐feedback form for both the finite and the infinite horizon formulations in terms of coupled Riccati differential and algebraic equations. A change of measures for both criteria and completion of squares method is used to derive the solutions, and explicit sufficient conditions for the admissibility of controls are derived. An application to the problem ofrobustportfolio control in a market with random interest rate subject to a disturbance is also given.