Optimal Control Response to Multiplicative Uncertainty with a Constant Term

In a one-state one-control variable Quadratic Linear Problem, I examine the effect of an increase in the multiplicative uncertainty on the use of the control variable. In contrast with previous studies, this model considers a stochastic constant term in the transition equation. I found that the optimal response depends on the covariance between the parameter with multiplicative uncertainty and the constant term. A nonnegative covariance produces a cautionary response following previous results. However, a negative covariance produces an aggressive response in the optimal control. Hence, previous studies represent a special case of this model. Numerical results are provided using global warming data