21 research outputs found
Continuous viscosity solutions to linear-quadratic stochastic control problems with singular terminal state constraint
This paper establishes the existence of a unique nonnegative continuous
viscosity solution to the HJB equation associated with a Markovian
linear-quadratic control problems with singular terminal state constraint and
possibly unbounded cost coefficients. The existence result is based on a novel
comparison principle for semi-continuous viscosity sub- and supersolutions for
PDEs with singular terminal value. Continuity of the viscosity solution is
enough to carry out the verification argument
Weak Solution for a Class of Fully Nonlinear Stochastic Hamilton-Jacobi-Bellman Equations
This paper is concerned with the stochastic Hamilton-Jacobi-Bellman equation
with controlled leading coefficients, which is a type of fully nonlinear
backward stochastic partial differential equation (BSPDE for short). In order
to formulate the weak solution for such kind of BSPDEs, the classical potential
theory is generalized in the backward stochastic framework. The existence and
uniqueness of the weak solution is proved, and for the partially non-Markovian
case, we obtain the associated gradient estimate. As a byproduct, the existence
and uniqueness of solution for a class of degenerate reflected BSPDEs is
discussed as well.Comment: 29 page