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 8

Numerical comparison between Proposition 2 and conditional Monte Carlo (CMC) approximation⁷.

	Proposition 2	CMC; 500,000	CMC; 5,000,000	CMC; 25,000,000
Average divergence (%)	0	0.57311	0.02378	0.00005
Maximum divergence (%)	0	1.09239	0.14412	0.00948
Computational time (seconds)	0.81	30.45	297.43	1436.76

The average divergence is the average of the absolute values of the differences between Proposition 2 and CMC divided by Proposition 2 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 2 and CMC divided by Proposition 2 out of a sample of 1,500 lists of randomly drawn parameters.
Computational time is measured on an i3 2.5 Ghz processor.