On the Computation of the Survival Probability of Brownian Motion with Drift in a Closed Time Interval When the Absorbing Boundary Is a Step Function

Table 1

Numerical comparison between Proposition 1 and conditional Monte Carlo (CMC) approximation¹.

	Proposition 1	CMC; 500,000	CMC; 5,000,000	CMC; 20,000,000
Average divergence (%)	0	0.29874	0.021496	0.00046
Maximum divergence (%)	0	0.84231	0.13884	0.087
Computational time (seconds)	0.59	24.57	239.26	953.42

The average divergence is the average of the absolute values of the differences between Proposition 1 and CMC divided by Proposition 1 out of a sample of 1,500 lists of randomly drawn parameters.
The maximum divergence is the maximum of the absolute values of the differences between Proposition 1 and CMC divided by Proposition 1 out of a sample of 1,500 lists of randomly drawn parameters.
Computational time is measured on an i3 2.5 Ghz processor.