Sensitivity of boundary crossing probabilities of the Brownian motion
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Abstract The paper analyzes the sensitivity of boundary crossing probabilities of the Brownian motion to perturbations of the boundary. The first- and second-order sensitivities, i.e. the directional derivatives of the probability, are derived. Except in cases where boundary crossing probabilities for the Brownian bridge are given in closed form, the sensitivities have to be computed numerically. We propose an efficient Monte Carlo procedure.
1999 ◽
Vol 36
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pp. 1019-1030
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1990 ◽
Vol 66
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pp. 489-502
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2005 ◽
Vol 50
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pp. 947-955
2005 ◽
Vol 26
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pp. 1725-1743
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1981 ◽
Vol 263
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pp. 469-469
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2010 ◽
Vol 47
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pp. 1058-1071
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