Business Description and Organization (Details)	12 Months Ended
	Dec. 31, 2017
Ownership structure of AB Holding
Limited partners or members ownership interest in Company (percent)	100.00%
AXA and its subsidiaries [Member]
Ownership structure of AB Holding
Limited partners or members ownership interest in Company (percent)	63.30%
AB Holding [Member]
Ownership structure of AB Holding
Limited partners or members ownership interest in Company (percent)	35.50%
Unaffiliated holders [Member]
Ownership structure of AB Holding
Limited partners or members ownership interest in Company (percent)	1.20%