Singular stochastic control and optimal stopping with partial information of jump diffusions
We study partial information, possibly non-Markovian, singular stochastic control of jump diffusions and obtain general maximum principles. The results are used to find connections between singular stochastic control, reflected BSDEs and optimal stopping in the partial information case. Mathematics Subject Classification 2010: 93E20, 60H07, 60H10, 60HXX, 60J75
Reflexion Discontinue et Systemes Stochastiques
We show the existence and uniqueness of the solution of stochastic equations of reflection on $\mathbb{R}^+_n$ associated to semimartingales with right continuous and left limited paths. This result is used to prove the existence and uniqueness of a Markov process associated with a boundary condition of Neumann type with degenerate infinitesimal generator.
A concept of general monotonicity and applications
In this paper we investigate properties of the general monotone sequences and functions, a generalization of monotone sequences and functions as well as of those of bounded variation. Some applications to various problems of analysis are given. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim