The Euler scheme for stochastic differential equations with discontinuous drift coefficient: a numerical study of the convergence rate

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 7 Discrete occupation rates for the discretized Atlas model

	T		Firm 1	Firm 2	Firm 3	Quadratic deviations
Y(0)	100	Rank 1	0.2911	0.2895	0.4194	0.0030	0.0031	0.0111
		Rank 2	0.3425	0.3662	0.2913
		Rank 3	0.3664	0.3443	0.2892
	250	Rank 1	0.3156	0.3161	0.3683	0.0005	0.0005	0.0018
		Rank 2	0.3375	0.3463	0.3162
		Rank 3	0.3469	0.3376	0.3155
	500	Rank 1	0.3238	0.3246	0.3517	0.0001	0.0001	0.0005
		Rank 2	0.3357	0.3400	0.3243
		Rank 3	0.3406	0.3354	0.3240
	750	Rank 1	0.3273	0.3273	0.3454	0.0001	0.0001	0.0002
		Rank 2	0.3347	0.3379	0.3274
		Rank 3	0.3380	0.3348	0.3272
	1000	Rank 1	0.3288	0.3287	0.3425	0.0000	0.0000	0.0001
		Rank 2	0.3344	0.3368	0.3288
		Rank 3	0.3368	0.3345	0.3287
Ỹ(0)	100	Rank 1	0.1464	0.1447	0.7089	0.0554	0.0562	0.2116
		Rank 2	0.3883	0.4654	0.1463
		Rank 3	0.4653	0.3899	0.1448
	250	Rank 1	0.2581	0.2579	0.4840	0.0090	0.0090	0.0341
		Rank 2	0.3555	0.3863	0.2582
		Rank 3	0.3864	0.3558	0.2577
	500	Rank 1	0.2949	0.2956	0.4096	0.0023	0.0023	0.0087
		Rank 2	0.3448	0.3599	0.2953
		Rank 3	0.3603	0.3446	0.2951
	750	Rank 1	0.3082	0.3079	0.3840	0.0010	0.0010	0.0038
		Rank 2	0.3407	0.3513	0.3081
		Rank 3	0.3511	0.3409	0.3080
	1000	Rank 1	0.3143	0.3142	0.3715	0.0006	0.0006	0.0022
		Rank 2	0.3391	0.3467	0.3143
		Rank 3	0.3467	0.3391	0.3143