2021/01/15 by Olivier Menoukeu Pamen, Menoukeu-Pamen, Olivier, Ludovic Tangpi +1
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Climate Change Policy and Economics #Mathematical Biology Tumor Growth
paper · pdf · doi:10.48550/arxiv.2101.06205
In this paper, we consider stochastic optimal control of systems driven by stochastic differential equations with irregular drift coefficient. We establish a necessary and sufficient stochastic maximum principle. To achieve this, we first derive an explicit representation of the first variation process (in Sobolev sense ) of the controlled diffusion. Since the drift coefficient is not smooth, the representation is given in terms of the local time of the state process. Then we construct a sequence of optimal control problems with smooth coefficients by an approximation argument. Finally, we use Ekeland's variational principle to obtain an approximating adjoint process from which we derive the maximum principle by passing to the limit.