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In this paper we study the finite-horizon optimal covariance steering problemfor a continuous-time linear stochastic system subject to both additive andmultiplicative noise. The noise can be continuous or it may contain jumps.Additive noise does not depend on the state or the control, whereasmultiplicative noise has a magnitude proportional to the current state. Thecost is assumed to be quadratic in both the state and the control. First, thecontrollability of the state covariance is established under mild assumptions.Then, the optimal control for steering the covariance is provided. Lastly, theexistence and uniqueness of the optimal control is shown. In the process, weprovide a result of independent interest regarding the maximal interval ofexistence of the solution to a matrix Riccati differential equation.

Optimal Covariance Steering for Continuous-Time Linear Stochastic Systems With Multiplicative Noise