Boundary crossing probability for Brownian motion
2001 ◽
Vol 38
(01)
◽
pp. 152-164
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Keyword(s):
Wang and Pötzelberger (1997) derived an explicit formula for the probability that a Brownian motion crosses a one-sided piecewise linear boundary and used this formula to approximate the boundary crossing probability for general nonlinear boundaries. The present paper gives a sharper asymptotic upper bound of the approximation error for the formula, and generalizes the results to two-sided boundaries. Numerical computations are easily carried out using the Monte Carlo simulation method. A rule is proposed for choosing optimal nodes for the approximating piecewise linear boundaries, so that the corresponding approximation errors of boundary crossing probabilities converge to zero at a rate of O(1/n 2).
2001 ◽
Vol 38
(1)
◽
pp. 152-164
◽
1997 ◽
Vol 34
(01)
◽
pp. 54-65
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2013 ◽
Vol 50
(02)
◽
pp. 419-429
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2013 ◽
Vol 50
(2)
◽
pp. 419-429
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1992 ◽
Vol 29
(02)
◽
pp. 448-453
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1999 ◽
Vol 36
(4)
◽
pp. 1019-1030
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2010 ◽
Vol 47
(4)
◽
pp. 1058-1071
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