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The four biggest U.S. private equity firms have a combined asset hoard of nearly $3 trillion, but within that big number, each is on a different quest. Blackstone, Carlyle, KKR and Apollo Global Management are all pursuing their own strategies, and their first-quarter financials showed them hitting some important new targets. Each, though, has ogres to vanquish. Apollo’s earnings on Thursday reflected its transformation into a gigantic private lender, powered by dollars from its in-house insurance business. Steady fees, which shareholders generally like, and income from investing policyholders’ premiums accounted for nearly all of net income. Apollo boss Marc Rowan wants its