Optimal regulator for linear stochastic systems with state-delay and random time-horizon
Nuha Alasmi, Bujar Gashi · 2024
We consider an optimal control problem for linear stochastic systems with state-delay, additive and multiplicative noise, and random time-horizon. We obtain an explicit closed-form solution to this problem for a general quadratic-linear cost functional through a system of coupled Riccati and partial differential equations. The optimal control law is of an affine feedback form with respect to the system state, the delayed state, and the integral of past system state values. An application to the optimal investment problem with a logarithmic utility and an interest rate with delayed factor process is also given.