Asymptotic analysis of optimal investment and consumption with transaction costs.
type: Item
instance of: scholarly article
title: Asymptotic analysis of optimal investment and consumption with transaction costs.
zbMATH Open document ID: 1098.91051
author: Karel Janeçek
author: Steven Shreve
published in: Finance and Stochastics
publication date: 2004-11-24T00:00:00Z
review text: The authors consider an agent seeking the optimally invest and consume in the presence of proportional transaction costs. The agent can invest in a stock modelled as a geometric Brownian motion and in a money market with constant rate of interest. He may also consume and get utility \(U(c)=c^{1-p}/(1-p)\), where \(p>0,\;p\neq 1\). In addition, the agent must pay a proportional transaction costs \(\lambda >0\) for transferring capital between the stock and the money market. All consumptions are done from the money market. The agent wishes to maximize the expected discounted integral over \([0,\infty)\) of the utility of consumption. To solve the problem, the authors heuristically derive several terms of a power series expansion of a value function in powers of \(\lambda^{1/3}\). Then the rigorous expansion is presented. The asymptotic results on the boundary of the ``no-trade'' region are obtained. The key results are proved using viscosity sub- and supersolutions.
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 60G44
zbMATH DE Number: 2118695
zbMATH Keywords: transaction costs
zbMATH Keywords: optimal control
zbMATH Keywords: asymptotic analysis
zbMATH Keywords: utility maximization
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: s00780-003-0113-4
OpenAlex ID: W1976551585
Wikidata QID: Q110634024
DOI: 10.1007/S00780-003-0113-4
description: scientific article; zbMATH DE number 2118695