Chapter

Models in Finance

GREGORY C. CHOW

in Dynamic Economics

Published in print April 1997 | ISBN: 9780195101928
Published online October 2011 | e-ISBN: 9780199855032 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780195101928.003.0007
Models in Finance

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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

Chapter.  10969 words. 

Subjects: Financial Markets

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