SIAM Journal on Control and Optimization, Vol.50, No.4, 2254-2287, 2012
SINGULAR STOCHASTIC CONTROL AND OPTIMAL STOPPING WITH PARTIAL INFORMATION OF ITO-LEVY PROCESSES
We study partial information, possibly non-Markovian, singular stochastic control of Ito-Levy processes and obtain general maximum principles. The results are used to find connections between singular stochastic control, reflected backward stochastic differential equations, and optimal stopping in the partial information case. As an application we give an explicit solution to a class of optimal stopping problems with finite horizon and partial information.
Keywords:singular stochastic control;maximum principles;reflected BSDEs;optimal stopping;partial information;Ito-Levy processes;jump diffusions