We study a class of discounted models of singular stochastic control. In this kind of models, not only the structure of cost function has been extended to some general type, but also the state can be represented as t...We study a class of discounted models of singular stochastic control. In this kind of models, not only the structure of cost function has been extended to some general type, but also the state can be represented as the solution of a class of stochastic differential equations with nonlinear drift and diffusion term. By the various methods of stochastic analysis, we derive the sufllcient and necessary conditions of the existence of optimal control.展开更多
We study the existence and uniqueness of the solution to a forward-backward stochastic differential equation with subdifferential operator in the backward equation. This kind of equations includes, as a particular cas...We study the existence and uniqueness of the solution to a forward-backward stochastic differential equation with subdifferential operator in the backward equation. This kind of equations includes, as a particular case, multi-dimensional forward-backward stochastic differential equation where the backward equation is reflected on the boundary of a closed convex(time-independent) domain. Moreover, we give a probabilistic interpretation for the viscosity solution of a kind of quasilinear variational inequalities.展开更多
基金This research is supported by the National Natural Science Foundation of China
文摘We study a class of discounted models of singular stochastic control. In this kind of models, not only the structure of cost function has been extended to some general type, but also the state can be represented as the solution of a class of stochastic differential equations with nonlinear drift and diffusion term. By the various methods of stochastic analysis, we derive the sufllcient and necessary conditions of the existence of optimal control.
基金supported by Australian Research Council’s Discovery Projects Funding Scheme(Grant No.DP120100895)
文摘We study the existence and uniqueness of the solution to a forward-backward stochastic differential equation with subdifferential operator in the backward equation. This kind of equations includes, as a particular case, multi-dimensional forward-backward stochastic differential equation where the backward equation is reflected on the boundary of a closed convex(time-independent) domain. Moreover, we give a probabilistic interpretation for the viscosity solution of a kind of quasilinear variational inequalities.
