Stopping Problems of Certain Multiplicative Functionals and Optimal Investment with Transaction Costs

Stopping Problems of Certain Multiplicative Functionals and Optimal Investment with Transaction... Optimal stopping and impulse control problems with certain multiplicative functionals are considered. The stopping problems are solved by showing the unique existence of the solutions of relevant variational inequalities. However, since functions defining the multiplicative costs change the signs, some difficulties arise in solving the variational inequalities. Through gauge transformation we rewrite the variational inequalities in different forms with the obstacles which grow exponentially fast but with positive killing rates. Through the analysis of such variational inequalities we construct optimal stopping times for the problems. Then optimal strategies for impulse control problems on the infinite time horizon with multiplicative cost functionals are constructed from the solutions of the risk-sensitive variational inequalities of "ergodic type" as well. Application to optimal investment with fixed ratio transaction costs is also considered. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Stopping Problems of Certain Multiplicative Functionals and Optimal Investment with Transaction Costs

Loading next page...
 
/lp/springer_journal/stopping-problems-of-certain-multiplicative-functionals-and-optimal-TKhcJo39gR
Publisher
Springer-Verlag
Copyright
Copyright © 2007 by Springer
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-006-0868-2
Publisher site
See Article on Publisher Site

Abstract

Optimal stopping and impulse control problems with certain multiplicative functionals are considered. The stopping problems are solved by showing the unique existence of the solutions of relevant variational inequalities. However, since functions defining the multiplicative costs change the signs, some difficulties arise in solving the variational inequalities. Through gauge transformation we rewrite the variational inequalities in different forms with the obstacles which grow exponentially fast but with positive killing rates. Through the analysis of such variational inequalities we construct optimal stopping times for the problems. Then optimal strategies for impulse control problems on the infinite time horizon with multiplicative cost functionals are constructed from the solutions of the risk-sensitive variational inequalities of "ergodic type" as well. Application to optimal investment with fixed ratio transaction costs is also considered.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: May 1, 2007

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off