Summary of Identifiable Assets and Equity (Detail) - USD ($) $ in Thousands	Mar. 31, 2021	Dec. 31, 2020	Mar. 31, 2020	Dec. 31, 2019
Segment Reporting Information [Line Items]
Identifiable Assets	$ 29,385,883	$ 28,927,010
Invested Assets and Cash	21,198,500
Equity Attributable to Alleghany	8,695,881	$ 8,755,720	$ 7,857,062	$ 8,776,734
Operating Segments
Segment Reporting Information [Line Items]
Identifiable Assets	28,371,100
Invested Assets and Cash	20,207,500
Equity Attributable to Alleghany	8,852,100
Operating Segments | Reinsurance Segment
Segment Reporting Information [Line Items]
Identifiable Assets	18,384,700
Invested Assets and Cash	14,662,600
Equity Attributable to Alleghany	5,251,900
Operating Segments | Insurance Segment
Segment Reporting Information [Line Items]
Identifiable Assets	7,477,300
Invested Assets and Cash	5,452,100
Equity Attributable to Alleghany	2,522,400
Operating Segments | Reinsurance Segment and Insurance Segment
Segment Reporting Information [Line Items]
Identifiable Assets	25,862,000
Invested Assets and Cash	20,114,700
Equity Attributable to Alleghany	7,774,300
Operating Segments | Alleghany Capital Corporation Segment
Segment Reporting Information [Line Items]
Identifiable Assets	2,509,100
Invested Assets and Cash	92,800
Equity Attributable to Alleghany	1,077,800
Corporate activities
Segment Reporting Information [Line Items]
Identifiable Assets	1,014,800
Invested Assets and Cash	991,000
Equity Attributable to Alleghany	$ (156,200)