Optimizing Rank-Dependent Utility Theory Computations: Algorithm Analysis with Applications to Firm Hedging Strategies

Abstract

[Abstract]: Rank-Dependent Utility Theory (RDU) provides a comprehensive alternative to Expected Utility Theory (EUT) for modeling decision-making under uncertainty. By incorporating probability weighting, RDU captures observed behavioral patterns that EUT fails to explain, offering both theoretical enhancements and empirical support. Despite its strengths, the practical application of RDU is often hindered by the complexity involved in calculating its functional values, making it less accessible for routine decision analysis. The primary challenge arises from the fact that, according to this theory, outcomes must be arranged by their magnitude, and each outcome’s weight is determined by the difference of a probability weighting function (pwf). This inherent structure makes calculating RDU values complex, even for relatively simple discrete random variables. This paper has two main objectives. First, it addresses gaps in the literature on RDU value computation and time complexity. While methods for calculating RDU exist, comprehensive algorithms and optimization techniques are lacking. We analyze the time complexity of various approaches and provide Python and R code for RDU computations and parameter optimization. Although closed-form solutions are generally unavailable for RDU, they are achievable for Yaari’s Dual Theory (DUT), a special case of RDU, using a proposed alternative algorithm. Second, we apply our findings to a practical case study, examining optimal hedging strategies for a real estate firm facing currency mismatches between revenue and costs. By considering decision-makers with varying psychological traits, such as optimism and pessimism, we explore how these traits influence the optimal hedging strategy and use sensitivity analysis to assess their impact.