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Arbitrage Theory in Continuous Time$
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Tomas Björk

Print publication date: 2004

Print ISBN-13: 9780199271269

Published to Oxford Scholarship Online: October 2005

DOI: 10.1093/0199271267.001.0001

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Differential Equations

Differential Equations

Chapter:
(p.62) 5 Differential Equations
Source:
Arbitrage Theory in Continuous Time
Author(s):

Tomas Björk (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0199271267.003.0005

This chapter examines whether there exists a stochastic process X, which satisfies the stochastic differential equation (SDE) d X t = μ (t, X t) d t + σ (t, X t) d W t, X 0 = x 0. The standard method for proving the existence of a solution to the SDE is to construct an iteration scheme of Cauchy-Picard type. Although the construction can be carried out, the proof requires some hard inequalities. Thus, only the result is given. Practice exercises are included.

Keywords:   stochastic process, differential equation, Cauchy-Picard iteration

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