Regime Shifts in Nonlinear Stochastic Optimal Control Problems∗

We develop a method of obtaining an asymptotic series of the value function of a stochastic optimal control problem over an unbounded domain with a finite number of irregularity points. These are points of non-differentiability of the value function of the corresponding deterministic problem. We apply singular perturbation methods to obtain the solution approximation in regions of regularity and use the method of matched asymptotic expansions to compose the approximation over the whole state domain. From this approximation, a geometric invariant transformation invariant function is computed. For problems with irregularity points this function is multimodal. This allows to define regime switching thresholds as its local minima. Our findings are applied to analyse the stochastic lake model. In particular, we show effects of changing the pollution costs and the discount rate on average durations of the two regimes: ‘clean lake’ and ‘polluted lake’. JEL codes: C61, Q57