A stochastic optimal control problem and its applications

Optimal Transportation Problem by Stochastic Optimal Control

We solve optimal transportation problem using stochastic optimal control theory. Indeed, for a super linear cost at most quadratic at infinity, we prove Kantorovich duality theorem by a zero noise limit (or vanishing viscosity) argument.. We also obtain a characterization of the support of an optimal measure in Monge-Kantorovich minimization problem (MKP) as a graph. Our key tool is a duality r...

Optimal Stochastic Control in Continuous Time with Wiener Processes: General Results and Applications to Optimal Wildlife Management

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...

Quantitative Determination Of Optimal Fiscal And Monetary Policies: A Stochastic Optimal Control Analysis For Iran

Stationary Hamilton--Jacobi Equations in Hilbert Spaces and Applications to a Stochastic Optimal Control Problem

We study an infinite horizon stochastic control problem associated with a class of stochastic reaction-diffusion systems with coefficients having polynomial growth. The hamiltonian is assumed to be only locally Lipschitz continuous so that the quadratic case can be covered. We prove that the value function V corresponding to the control problem is given by the solution of the stationary Hamilto...

A Nonconvex Singular Stochastic Control Problem and its Related Optimal Stopping Boundaries

Equivalences are known between problems of singular stochastic control (SSC) with convex performance criteria and related questions of optimal stopping, see for example Karatzas and Shreve [SIAM J. Control Optim. 22 (1984)]. The aim of this paper is to investigate how far connections of this type generalise to a non convex problem of purchasing electricity. Where the classical equivalence break...