In the years after Jeffrey Epstein registered as a sex offender, he closed his money management firm and started a business to develop algorithms and mine DNA and financial databases.

Then he set up a bank.

In a banking license application reviewed by The New York Times, Mr. Epstein described himself as one of the investing world’s “pioneers” and said he wanted to pursue the “dynamic discipline of international banking.”

Officials in the Virgin Islands, the United States territory where Mr. Epstein set up most of his businesses, approved a license for him in 2014 to run one of the territory’s first international banking entities, a specialized bank that can do business only with offshore clients. The approval was unusual, given Mr. Epstein’s status as a convicted sex offender.

The bank, Southern Country International, renewed its license for each of the next five years, but it’s unclear whether it conducted any business or had any customers. Mr. Epstein, who died while in federal custody last summer following his arrest on sex trafficking charges, does not appear to have done any marketing for the bank or hired much staff.