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Register a new userComputing wedge probabilities: finite time horizon case
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Authors
Dmitry Muravey
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We present an alternative to the well-known Andersons formula for the probability that a first exit time from the planar region between two slopping lines -a_1 t -b_1 and a_2 t + b_2 by a standard Brownian motion is greater than T. As the Andersons formula, our representation is an infinite series from special functions. We show that convergence rate of both formulas depends only on terms (a_1 + a_2)(b_1 + b_2) and (b_1 + b_2)^2 /T and deduce simple rules of appropriate representations choose. We prove that for any given set of parameters a_1, b_1, a_2, b_2, T the sum of first 6 terms ensures precision 10^{-16}.
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These notes are the second half of the contents of the course given by the second author at the Bachelier Seminar (8-15-22 February 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis.
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