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
Singular control of SPDEs and backward SPDEs with reflection
In the first part, we consider general singular control problems for random fields given by a stochastic partial differential equation (SPDE). We show that under some conditions the optimal singular control can be identified with the solution of a coupled system of SPDE and {\it a kind of reflected backward} SPDE (RBSPDE).In the second part, existence and uniqueness of solutions of RBSPDEs are established, which is of independent interest.
A UNIVERSAL OPTIMAL CONSUMPTION RATE FOR AN INSIDER
We consider a cash flow X(c) (t) modeled by the stochastic equation where B(·) and are a Brownian motion and a Poissonian random measure, respectively, and c(t) ≥ 0 is the consumption/dividend rate. No assumptions are made on adaptedness of the coefficients μ, σ, θ, and c, and the (possibly anticipating) integrals are interpreted in the forward integral sense. We solve the problem to find the consumption rate c(·), which maximizes the expected discounted utility given by Here δ(t) ≥ 0 is a given measurable stochastic process representing a discounting exponent and τ is a random time with values in (0, ∞), representing a terminal/default time, while γ≥ 0 is a known constant.