Business segment data - Insurance premiums by geographic area (Detail) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Property/Casualty [Member]
Segment Reporting Information [Line Items]
Premiums written	$ 58,473	$ 56,971	$ 52,614
Life/Health [Member]
Segment Reporting Information [Line Items]
Premiums written	6,428	5,840	6,602
United States [Member] | Property/Casualty [Member]
Segment Reporting Information [Line Items]
Premiums written	50,250	50,529	46,146
United States [Member] | Life/Health [Member]
Segment Reporting Information [Line Items]
Premiums written	2,820	2,553	3,598
Asia Pacific [Member] | Property/Casualty [Member]
Segment Reporting Information [Line Items]
Premiums written	3,410	3,114	3,726
Asia Pacific [Member] | Life/Health [Member]
Segment Reporting Information [Line Items]
Premiums written	1,652	1,582	1,361
Western Europe [Member] | Property/Casualty [Member]
Segment Reporting Information [Line Items]
Premiums written	3,751	2,535	2,157
Western Europe [Member] | Life/Health [Member]
Segment Reporting Information [Line Items]
Premiums written	1,120	908	939
All Other [Member] | Property/Casualty [Member]
Segment Reporting Information [Line Items]
Premiums written	1,062	793	585
All Other [Member] | Life/Health [Member]
Segment Reporting Information [Line Items]
Premiums written	$ 836	$ 797	$ 704