Shares in the bank had jumped 3.65 percent in Frankfurt by just after 0800 GMT on the news, recouping a fraction of the heavy losses suffered on Monday and Tuesday.
Regulators must still approve the 935-million-pound (USD 1.2-billon) sale, the bank said.
Deutsche Bank said in a statement that the sale would boost its core capital ratio -- the stock of funds regulators require banks to have on hand -- by 10 basis points, or 0.1 per cent over its level on June 30.
The announcement comes after shares in the bank hit a record low on Monday, dropping 7.54 percent to close at 10.55 euros (USD 11.80) amid growing fears over its capital cushion.
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Investors are nervous after it emerged earlier this month that the US Department of Justice is seeking a $14-billion fine from Deutsche over its role in the subprime mortgage crisis.
Following the sale of Abbey Life, subsidiary Deutsche Asset Management "will continue to concentrate on its core business," bank chief John Cryan said in a statement.
Cryan launched a drastic restructuring programme at Deutsche after taking office 15 months ago, as Germany's biggest lender continues to struggle with the fallout of the financial crisis.
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