Section: New Results

Optimal control of Stochastic Partial Differential equations (SPDEs)

SPDEs appear in the modeling of a number of situations: for example, in dynamic pollution models, in financial models involving interest rate derivatives, in systemic risk modeling. The research issues include optimal control of SPDEs and nonlinear filtering theory, stochastic control of forward-backward systems of SPDEs with imperfect and/or asymmetric information, optimal stochastic control of mean-field systems of SPDEs. We have started to study singular control of SPDEs. We plan to give a method for solving optimal control problems for general, possibly non-Markovian systems of FBSDEs by means of BSPDEs with jumps and associated comparison theorems.