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Dynamic EconomicsOptimization by the Lagrange Method$
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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

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Models in Finance

Models in Finance

Chapter:
(p.139) Chapter Seven Models in Finance
Source:
Dynamic Economics
Author(s):

GREGORY C. CHOW

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195101928.003.0007

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

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