Jump to ContentJump to Main Navigation
Dynamic EconomicsOptimization by the Lagrange Method$
Users without a subscription are not able to see the full content.

Gregory C. Chow

Print publication date: 1997

Print ISBN-13: 9780195101928

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780195101928.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 14 October 2019

Models in Finance

Models in Finance

(p.139) Chapter Seven Models in Finance
Dynamic Economics


Oxford University Press

Using stochastic differential equations instead of utilizing stochastic difference equations, most of the models involved in finance follow Merton’s work and are developed in continuous time. In this chapter, an alternative stochastic differential equation is introduced to replace the vector for state variables. The chapter introduces the Wiener process in which a change in the time variable is perceived to be normally distributed and with zero mean. After illustrating how dynamic programming is employed in a model that involves continuous time, we look into the illustration included in this chapter about how to solve such problems using the method of Lagrange multipliers. We also attempt to examine the optimal control function, optimum consumption, and other issues such as capital asset pricing in the event of shifts in investments.

Keywords:   differential equations, Merton, state variables, Wiener process, Lagrange multipliers

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .