The United States and Europe will issue record levels of i.o.u.’s as governments finance deficits and rescues.

The decision to go public is the latest twist for Kohlberg Kravis Roberts & Company, a firm that helped invent an entire industry.

The plan would value the storied private equity firm at $12 billion to $15 billion and is part of a complex deal in which it will buy its publicly traded affiliate, KKR Private Equity Investors.

Kohlberg Kravis Roberts & Company, the giant buyout firm, plans to announce a new partnership with the Environmental Defense Fund.