A leavable bounded-velocity stochastic control problem.
type: Item
instance of: scholarly article
title: A leavable bounded-velocity stochastic control problem.
zbMATH Open document ID: 1064.93049
DOI: 10.1016/S0304-4149(01)00157-0
author: Ioannis Karatzas
author: Daniel L. Ocone
published in: Stochastic Processes and their Applications
publication date: 2005-02-25T00:00:00Z
review text: The paper studies solutions to optimal control of the drift of a diffusion process that can be stopped arbitrarily. Accordingly, the minimized objective function of the control problem consists of the expected running cost and exit cost terms. Both fully observed and partially observed state process cases are considered. In the fully observed case, the bang-bang controls and the optimal stopping regions are identified for a class of strictly convex cost functions. The value function is derived and the optimal behavior is shown to be heavily dependent upon the relative weight of exit cost. The control of a partially observed state process is considered for cost functions of polynomial growth, separately for finite and infinite horizon cases. It is established that when stopping at a given level of the state is optimal in the infinite horizon problem, doing so is also optimal in any finite horizon problem as well. Further, it is shown that for any horizon, finite or infinite, the optimal stopping region of the fully observed control is included in the one of the partially observed control.
reviewed by: Alexis Derviz
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 2138961
zbMATH Keywords: stochastic control
zbMATH Keywords: discretionary stopping
zbMATH Keywords: bang-bang control
zbMATH Keywords: partially observed state
MaRDI profile type: Publication
cites work: Composition and invariance methods for solving some stochastic control problems
cites work: Q3360769
cites work: Some solvable stochastic control problemst†
cites work: Q3935745
cites work: A problem of singular stochastic control with discretionary stopping
cites work: Q4131339
cites work: A comparison theorem for solutions of stochastic differential equations and its applications
cites work: Q3992729
cites work: Hedging American contingent claims with constrained portfolios
cites work: The resolvent of a degenerate diffusion on the plane, with application to partially observed stochastic control
cites work: The finite–horizon version for a partially–observed stochastic control problem of benesš & rishel
cites work: Q4002114
cites work: A barrier option of American type
cites work: Utility Maximization with Discretionary Stopping
cites work: Finite-Fuel Singular Control With Discretionary Stopping
cites work: Q3910361
cites work: Q4881151
cites work: Variational Inequalities for Combined Control and Stopping
cites work: Optimal Stopping of One-Dimensional Diffusions
cites work: Optimal Stopping in a Markov Process
full work available at URL: s0304-4149(01)00157-0
OpenAlex ID: W1977844252
description: scientific article; zbMATH DE number 2138961