“…a central bank, can change the interest rate according to macroeconomic variables, as the country inflation level, the forecast of supranational interest rates, the the markets' belief about the health of the financial sector under the central bank control, etc. In fact, choosing α = 0 the bank value grows at rate µ(t), which is strictly greater than µ(t) − α(t) for a given control 0 < α(t) ≤ r. We refer to the above discussion, see also, e.g., [2,3,8,9,47,37,19], for more financially oriented ideas supporting the latter setting. Accordingly, we can assume that the controller aims at maximizing a functional of the following type…”