2023/07/31 by Nacira Agram, Bernt Øksendal, Agram, Nacira +5
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2308.00173
In this paper we study a Pontryagin type stochastic maximum principle for the optimal control of a system, where the state dynamics satisfy a stochastic partial differential equation (SPDE) driven by a two-parameter (time-space) Brownian motion (also called Brownian sheet). We first discuss some properties of a Brownian sheet driven linear SPDE which models the growth of an ecosystem. Further, applying time-space white noise calculus we derive sufficient conditions and necessary conditions of optimality of the control. Finally, we illustrate our results by solving a linear quadratic control problem and an optimal harvesting problem in the plane. We also study possible applications to machine learning.