In this short note, we show that the results presented by Jindapon and Neilson (2007) for changes in risk à la Ekern (1980) can be extended to stochastic dominance changes, with appropriate additional conditions on the utility function
Denuit, M., & Eeckoudt, L. (2012). Improving your chances: An extension of Jindapon and Neilson (2007) (ISBA Discussion Paper 2012/08). https://hdl.handle.net/2078.5/208561