Taylor expansions of curve-crossing probabilities

Hobson, David G.; Williams, David; Wood, Andrew T.A.

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Taylor expansions of curve-crossing probabilities

Date

1999

Authors

Hobson, David G.

Williams, David

Wood, Andrew T.A.

Abstract

Using an approach based on the Cameron-Martin-Girsanov theorem, we obtain a Taylor expansion for the probability that Brownian motion hits a smooth nonlinear boundary which grows at a suitable rate. The structure and probabilistic meaning of the terms in the expansion are studied in some detail.