control problem and equilibrium determination. Our social planner may consider to increase his investment at any stopping time …, which completes the proof. The intuition conveyed by the rst order condition reveals the connection between the optimal …

many others. As a canonical general approach for solving an optimal control problem one may consider all possible future … Par(Xr,dy) which is in turn controlled by ar. In this setting we may consider the general optimal control problem (2.1) Y … the optimal control problem (2.2) Y∗0 = sup a∈A,τ∈T Ea bracketleftBiggτ−1summationdisplay r=0 fr …