EconPapers    
Economics at your fingertips  
 

A finite difference scheme for variational inequalities arising in stochastic control problems with several singular control variables

Hidekazu Yoshioka and Yuta Yaegashi

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 156, issue C, 40-66

Abstract: A finite difference scheme is developed for solving 1-D variational inequalities arising in stochastic control problems with several singular control variables. The scheme guarantees the uniqueness of numerical solutions. A policy iteration algorithm is then proposed to solve the discretized problem. The present approach is applied to solving variational inequalities associated to cost-effective management problems of benthic algae on the riverbed downstream of a dam: an urgent environmental problem. Accuracy of the scheme is verified to be first-order for both the solution and its free boundaries. An advanced problem that involves a max–min differential game structure is also examined. The scheme then computes reasonably accurate numerical solutions which are consistent with the theoretical asymptotic estimates.

Keywords: Finite difference scheme; Singular stochastic control; Variational inequality; Free boundary; Stochastic differential game (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475418301708
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:156:y:2019:i:c:p:40-66

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Dana Niculescu ().

 
Page updated 2019-01-19
Handle: RePEc:eee:matcom:v:156:y:2019:i:c:p:40-66