Loss-Aversion with Kinked Linear Utility Functions

Abstract

Prospect theory postulates that the utility function is characterized by a kink (a point of non-differentiability) that distinguishes gains from losses. In this paper we present an algorithm that efficiently solves the linear version of the kinked-utility problem. First, we transform the non-differentiable kinked linear-utility problem into a higher dimensional, differentiable, linear program. Second, we introduce an efficient algorithm that solves the higher dimensional linear program in a smaller dimensional space. Third, we employ a numerical example to show that solving the problem with our algorithm is 15 times faster than solving the higher dimensional linear program using the interior point method of Mosek. Finally, we provide a direct link between the piece-wise linear programming problem and conditional value-at-risk, a downside risk measure.