Research On Singular Optimal Control Problems In Uncertain Systems

Some classes of singular stochastic optimal control problems in uncertain systems are treated in this thesis.This thesis is divided into the following six sections.Section 1 In this section, some notations used in this thesis are given. The origin and developments of the theory of stochastic optimal control are introduced, as well as some common stochastic optimal control models.Section 2 In this section, a class of singular stochastic optimal control models with discounted cost are studied. In this class of models, the control action on the control target towards positive and negative direction is separated into two parts.Section 3 In this section, a class of singular stochastic optimal control models in proportional reinsurance problems are studied. In this class of models, dividend pay-out, corporate debts, and bankruptcy compensation are considered.Section 4 In this section, a class of singular stochastic optimal control models in financing problems are studied. In this class of models, dividend pay-out, transaction costs, corporate income tax, and corporate debts are considered.Section 5 In this section, a class of singular stochastic optimal control models in harvesting problems are studied. In this class of models, the size of the people is the solution to a logistic stochastic differential equation.Section 6 In this section, a summary of the whole thesis is given, as well as the hope for deeper research works.