A leavable bounded-velocity stochastic control problem

A Leavable Bounded-velocity Stochastic Control Problem

This paper studies bounded-velocity control of a Brownian motion when discretionary stopping, or ‘leaving’, is allowed. The goal is to choose a control law and a stopping time in order to minimize the expected sum of a running and a termination cost, when both costs increase as a function of distance from the origin. There are two versions of this problem: the fully-observed case, in which the ...

Approximation of a Stochastic Ergodic Control Problem

We study a degenerate non linear optimal stochastic control problem of ergodic type. We rst prove that for each feedback control law, there exists a unique invariant measure which is equivalent to Lebesgue measure. This is proved using an accessibility property of the stochastic diierential equation, after the discontinuous part of the drift has been removed via a change of probability measure....

A stochastic control problem for SNLPs

On a Non-Standard Stochastic Control Problem

Abstract. This paper considers the Merton portfolio management problem. We are concerned with non-exponential discounting of time and this leads to time inconsistencies of the decision maker. Following [6] we introduce the notion of equilibrium policies and we characterize them by an integral equation. The main idea is to come up with the value function in this context. If risk preferences are ...

Stochastic Optimal Control Problems with a Bounded Memory∗

This paper treats a finite time horizon optimal control problem in which the controlled state dynamics is governed by a general system of stochastic functional differential equations with a bounded memory. An infinite-dimensional HJB equation is derived using a Bellman-type dynamic programming principle. It is shown that the value function is the unique viscosity solution of the HJB equation. I...