It is known that optimal stopping problems form an important class of optimal control problems having applications in stochastic calculus (maximal inequalities), statistics (sequential analysis) and mathematical finance (American options). The results about the relationship between optimal stopping problems for Markov processes and free-boundary problems for partial differential equations often...

Controlled discrete-time stochastic processes are studied using the convex-analytic approach. Some new properties of strategic measures spaces are established, particular Markov models are considered. The meaningful example is presented.

The purpose of this paper is twofold: i) to introduce the sufficient statistic algebra which is responsible for propagating the sufficient statistics, or information state, in the optimal control of stochastic systems and ii) to apply certain Lie algebraic methods and gauge transformations, widely used in nonlinear control theory and quantum physics, to derive new results concerning finite-dime...

We consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled backward stochastic differential equation. Under appropriate convexity assumptions on the coefficients of the forward and the backward equations we prove the existence of an optimal control on a suitable reference stoch...

<p style='text-indent:20px;'>This is a concise introduction to stochastic optimal control theory. We assume that the readers have basic knowledge of real analysis, functional elementary probability, ordinary differential equations and partial equations. will present following topics: (ⅰ) A brief presentation relevant results on analysis; (ⅱ) Formulation problems; (ⅲ) Variational method Po...

We present a stochastic optimal control approach to wildlife management. The objective value is the present value of hunting and meat, reduced by the present value of the costs of plant damages and traffic accidents caused by the wildlife population. First, general optimal control functions and value functions are derived. Then, numerically specified optimal control functions and value func...