We develop a new class of utility functions, sahara utility, with the distinguishing feature that it allows absolute risk aversion to be non-monotone and implements the assumption that agents may become less risk averse for very low values of wealth. The class contains the well-known exponential and power utility functions as limiting cases. We investigate the optimal investment problem under sahara utility and derive the optimal strategies in an explicit form using dual optimization methods. We also show how sahara utility functions extend the class of contingent claims that can be valued using indifference pricing in incomplete markets.
Pelsser, A. A. J., Chen, A., & Vellekoop, M. (2011). Modelling Non-Monotone Risk Aversion Using SAHARA Utility Functions. Journal of Economic Theory, 146(5), 2075-2092. https://doi.org/10.1016/j.jet.2011.06.011