Prospect theory, indifference curves, and hedging risks

The prospect theory is one of the most popular decision-making theories. It is based on S-shaped utility functions, unlike the von Neumann and Morgenstern (NM) theory, which is based on concave utility functions. The S-shaped functions bring challenges, and extensions and generalizations of the NM theory into the prospect theory are not always possible. For example, in the prospect theory, the monotonicity of indifference curves depends on the underlying mean, unlike in the NM theory. Risk-hedging decisions also become more complex within the prospect theory. In this paper, we discuss these topics and establish general results concerning certain covariances from which we can in turn infer properties of indifference curves and hedging decisions within the prospect theory.