Irreversible capital accumulation with economic impact
type: Item
instance of: scholarly article
title: Irreversible capital accumulation with economic impact
zbMATH Open document ID: 1373.49019
author: Hessah Al Motairi
author: Mihail Zervos
published in: Applied Mathematics and Optimization
publication date: 2017-08-10T00:00:00Z
review text: The authors consider an irreversible capacity expansion model which is a special case of a more general model [\textit{T. Ø. Kobila}, Stochastics Stochastics Rep. 43, No. 1--2, 29--63 (1993; Zbl 0825.93981)]. Market uncertainty is modeled by a geometric Brownian motion and additional investment is assumed to have a strictly negative effect on an underlying economic indicator process. The authors formulate an optimization problem which becomes a singular stochastic control problem [\textit{V. E. Benes} et al., Stochastics 4, 39--83 (1980; Zbl 0451.93068)] and an explicite solution is found using the Hamilton-Jacobi-Bellman machinery. The changes in the state process caused by optimal control action are proportional to the state process itself. Although interesting from stochastic control theory perspective the results seem to be too complicated from the economy point of view.
Mathematics Subject Classification ID: 49J55
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 49L99
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 91B26
Mathematics Subject Classification ID: 60G35
zbMATH DE Number: 6759150
zbMATH Keywords: singular stochastic control
zbMATH Keywords: HJB machinery
zbMATH Keywords: market models
zbMATH Keywords: capacity expansion
zbMATH Keywords: variational inequality
zbMATH Keywords: irreversible investment
Wikidata QID: Q59614424
reviewed by: Andrzej Świerniak
MaRDI profile type: Publication
full work available at URL: s00245-016-9341-9
OpenAlex ID: W2289950472
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DOI: 10.1007/S00245-016-9341-9
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