Irreversible investment problems
type: Item
instance of: scholarly article
title: Irreversible investment problems
zbMATH Open document ID: 0957.60085
author: Anders Øksendal
published in: Finance and Stochastics
publication date: 2000-11-01T00:00:00Z
full work available at URL: http://hdl.handle.net/10852/42684
review text: This paper focuses on the problem of investing in an uncertain market, when the investments are considered to be irreversible. This means that once an investment has been made and the market later drops to a less favorable state, one cannot undo the investment. The risk of overinvesting means that we should wait longer to invest, than if the investments were totally or partially reversible. On the other hand one does not want to wait too long and miss out on any profits due to our lack of capacity. The problem then is to find a proper investment strategy taking the fluctuating marked into account. Numerous examples of irreversible investments exist, for example purchase of highly specified production machinery, educating staff members or spending money on advertising. It is assumed that the investments have two effects on given economy. The first is that the income will increase. The other effect of an investment is obviously that it costs money. It is also assumed that an investment has different costs depending on what the capacity is and naturally also depending on how much one wants to increase the capacity. The author gives some implicit conditions for a solution in the case where the market process is \(n\)-dimensional and an explicit solution in the one-dimensional case. This paper uses the theory developed by \textit{E. B. Dynkin} [``Markov processes''. Vol. I, II (1965; Zbl 0132.37701)]\ to solve the problem. The paper also provides some generalization to find the specific solution to the irreversible investment problem.
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 1524268
zbMATH Keywords: optimal stochastic control
zbMATH Keywords: irreversible investments
zbMATH Keywords: monotone increasing controls
zbMATH Keywords: Feller processes
MaRDI profile type: Publication
OpenAlex ID: W2156374236
DOI: 10.1007/S007800050013
description: scientific article; zbMATH DE number 1524268