Two-moment decision models and utility-representable preferences: a comment on Bar-Shira and Finkelshtain

A further remark on two-moment decision models and utility-representable preferences

“…In their seminal paper Bar-Shira and Finkelshtain (1999) claimed that the indifference curve slope is increasing in σ if preferences display decreasing absolute risk aversion (DARA). Gelles and Mitchell (2002) prove that BF's claim is not correct and that a second assumption, namely the convexity of preferences, has to be added to ensure S σ (·) > 0. However, in their reply Bar-Shira and Finkelshtain (2002) introduce a concept of proper risk aversion and show that S(µ, σ) is increasing (decreasing) in σ if V increases in µ and the preference relation exhibits properness (improperness); compare BF's sufficient condition II.…”