Stochastic control problems where small intervention costs have big effects
type: Item
instance of: scholarly article
title: Stochastic control problems where small intervention costs have big effects
zbMATH Open document ID: 0938.93063
published in: Applied Mathematics and Optimization
publication date: 2000-06-27T00:00:00Z
full work available at URL: http://hdl.handle.net/10852/42926
review text: This paper deals with impulse control problems with the cost given by \(c+\lambda|\xi|\), where \(\xi\) is the size of the impulse and \(c\) and \(\lambda\) are positive constants. The author investigates how the value function \(V_c(y)\) depends on \(c\), where \(y\) is the starting point of the system, and he shows that (1) as \(c\) tends to \(0\), \(V_c\) converges to the value function for the corresponding singular stochastic control problem, (2) \(V_c\) is not differentiable at \(c=0\), precisely \({dV_c\over dc} (y)= \infty\) for all \(y\). This means that going from \(c=0\) to a small positive \(c\) can have a big effect on the value function.
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 1369642
zbMATH Keywords: quasi-variational inequality
zbMATH Keywords: nonrobustness feature
zbMATH Keywords: impulse control
zbMATH Keywords: value function
zbMATH Keywords: singular stochastic control
Wikidata QID: Q113187202
author: B. Øksendal
reviewed by: Makiko Nisio
MaRDI profile type: Publication
OpenAlex ID: W1974085046
DOI: 10.1007/S002459900130
description: scientific article; zbMATH DE number 1369642