Stochastic Programming Models for Decreasing Risk Aversion

For a stochastic programming problem with simple recourse, we show how to formulate and analyze a model that encodes the common risk attitude of decreasing risk aversion. We discuss a class of linear fractional utility functions that represent this risk attitude and show that for such a utility function the resulting nonlinear model can be reduced to a linear programming model. The linear model, moreover, has only a slight percentage increase in the number of constraints as compared with the usual linear model representing risk neutrality.