When it comes to modeling preferences in uncertainty, the usual choice is usually between constant absolute risk aversion (CARA, with an exponential function) and constant relative risk aversion (CRRA, with a power function). That is somewhat limiting, especially when one needs to cover a rather wide domain, as there is then no reason to believe risk aversion remains constant.
Masako Ikefuji, Roger Laeven, Jan Magnus and Chris Muris come up with a mixture, which they name Burr utility. It is CRRA at the origin and CARA at infinity and is a function that has some familiarity for those who use subsistence consumption (Stone-Geary utility function) except that this constant term is added. This implies in particular that marginal utility is never infinite, which is a property I am not sure I want to miss.