Carlyle Group, the politically influential private equity firm, on Thursday agreed to pay $20m following an investigation by Andrew Cuomo, New York attorney-general, into alleged corruption at the state’s biggest public pension fund.

Carlyle also agreed to a code of conduct promoted by Mr Cuomo that would ban use of outside agents to solicit public pension funds and prevent asset managers doing business with such funds for two years after making political donations to officials who could influence them.