Online Appendix: Skewness Preferences in Choice under Risk

Abstract

This online appendix (OA) contains proofs and additional results to the paper Ebert and Karehnke (2021) “Skewness Preferences in Choice under Risk.” Online Appendix OA.1 shows the proofs of the results in the main text. Online Appendix OA.2 studies behavioral implications of the orders of skewness-seeking and how they determine the trade-off of skewness against mean or variance. Online Appendix OA.3 characterizes skewness preferences in leading theories of choice under risk. It completes the analysis of expected utility (EU), rank-dependent utility (RDU), and cumulative prospect theory (CPT) in main text, and further covers moment-based, context-dependent, and belief-based theories of choice under risk. Online Appendix OA.4 provides an extensive analysis of the skewness preferences induced by probability weighting, as in RDU and CPT. Online Appendix OA.5 proposes two new utility functions that yield second-order skewness-seeking EU. Online Appendix OA.6 clarifies the relationship between the orders of skewness preference, the skewness risk premium, and the willingness to pay for skewness. Online Appendix OA.7 illustrates and discusses some technical aspects of this paper that concern the use and computation of one-sided derivatives. Online Appendix OA.8 presents the proofs to all results in the online appendix.