A Variational Approach To Stochastic Optimal Control Via State Moment Equations And Application

By using a very simple remark on the moment equations of stochastic processes, one can use the Euler-Lagrange variational approach to solve some stochastic optimal control problems. In stochastic optimal control, strictly speaking, Euler-Lagrange variational calculus does not apply, and one has to use value function approach. Unfortunately, on the practical standpoint, the partial differential equation so obtained is not very manageable. In the approach, the new state variable is the deviation from the nominal trajectory. The new dynamical equation and the new cost functions may be translated into the deterministic problem of a differential equation, and it is easy to solve. In the thesis, this approach is applicated in the stochastic economics, which include the problem on the retailer's ordering policy for commodities with stochastic demand, the optimal investment and consumption problem and the optimal control policy of reinsurance model.In the first problem,the thesis studies inventory management of commodities according to the research of stochastic demand with service income management on perishable commodities in network environment, which aims to find order quantity that maximizes the retailer's expected profit with stochastic demand.In the second problem, the optimal investment and consumption problem is to maximize the expected-utility about the consumption and terminal wealth extreme in fixed time domail.At last, we discuss a class of proportional reinsurance model with dividend process and also provide their optimal policies.