Abstract. We study partial information, possibly non-Markovian, singular stochastic control of Itô–Lévy 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 ...

Topics in Stochastic Control with Applications to Finance

Say that two sentences are factually equivalent when they describe the same facts or situations, understood as worldly items, i.e. as bits of reality rather than as representations of reality. The notion of factual equivalence is certainly of central interest to philosophical semantics, but it plays a role in a much wider range of philosophical areas. What is the logic of factual equivalence? T...

We study the problem on optimal harvesting from a population in a stochastic crowded environment with harvesting cost. In this problem, the size of the population satisfy the stochastic logistic differential equation, which serves as a model for population growth in a stochastic environment with finite carrying capacity when harvesting is exercised. We consider the following problem: What harve...

We consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled backward stochastic differential equation. Under appropriate convexity assumptions on the coefficients of the forward and the backward equations we prove the existence of an optimal control on a suitable reference stoch...

Strengthening a theorem of Hjorth this paper gives a new characterization of which Polish groups admit compatible complete left invariant metrics. As a corollary it is proved that any Polish group without a complete left invariant metric has a continuous action on a Polish space whose associated orbit equivalence relation is not essentially countable.