C{A|R}RA utility

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.