Singular Control and Optimal Stopping of SPDEs, and Backward SPDEs with Reflection
نویسندگان
چکیده
منابع مشابه
Singular Control and Optimal Stopping of SPDEs, and Backward SPDEs with Reflection
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 a reflected backward SPDE (RBSPDE). As an illustration we apply the result to a singular optimal harvesting problem from a population whose d...
متن کاملSingular 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 a kind of reflected backward SPDE (RBSPDE).In the second part, existence and uniqueness of solutions of RBSPDEs are establ...
متن کاملWhite noise driven SPDEs with reflection
We study reflected solutions of a nonlinear heat equation on the spatial interval [0, 1] with Dirichlet boundary conditions, driven by space-time white noise. The nonlinearity appears both in the drift and in the diffusion coefficient. Roughly speaking, at any point (t, x) where the solution u(t, x) is strictly positive it obeys the equation, and at a point (t, x) where u(t, x) is zero we add a...
متن کاملWhite noise driven quasilinear SPDEs with reflection
We study reflected solutions of the heat equation on the spatial interval [-0, 1] with Dirichlet boundary conditions, driven by an additive space-time white noise. Roughly speaking, at any point (x, t) where the solution u(x, t) is strictly positive it obeys the equation, and at a point (x, t) where u(x, t) is zero we add a force in order to prevent it from becoming negative. This can be viewed...
متن کاملA Non-Markovian Liquidation Problem and Backward SPDEs with Singular Terminal Conditions
We establish existence, uniqueness and regularity of solution results for a class of backward stochastic partial differential equations with singular terminal condition. The equation describes the value function of non-Markovian stochastic optimal control problem in which the terminal state of the controlled process is pre-specified. The analysis of such control problems is motivated by models ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Operations Research
سال: 2014
ISSN: 0364-765X,1526-5471
DOI: 10.1287/moor.2013.0602