Athene Holding Ltd., untested at running pension funds, wants to compete with the industry’s oldest and biggest firms. Jumping into the business of owning retirement plans would benefit Apollo Global Management LLC, the New York-based private equity shop led by billionaire Leon Black. Athene, co-created by Black’s firm eight years ago, would pay Apollo to manage the pension money. Companies looking to make employee-pension funds someone else’s challenge have sold them to giant insurers such as Prudential Financial Inc. and MetLife Inc.