Chapter

Differential Equations

Tomas Björk

in Arbitrage Theory in Continuous Time

Second edition

Published in print March 2004 | ISBN: 9780199271269
Published online October 2005 | e-ISBN: 9780191602849 | DOI: http://dx.doi.org/10.1093/0199271267.003.0005

Series: Oxford Finance Series

Differential Equations

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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

Chapter.  6941 words.  Illustrated.

Subjects: Financial Markets

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