Delayed Probabilistic Risk Attitude: A Parametric Approach

Pan, J.; Webb, C.; Zank, H.

Abstract

Experimental studies suggest that individuals exhibit more risk aversion in choices among prospects when the payment and resolution of uncertainty are immediate relative to when it is delayed. This leads to preference reversals that cannot be attributed to discounting. When data suggest that utility is time-independent, probability weighting functions, such as those used to model prospect theory preferences, can accommodate such reversals. We propose a simple descriptive model with a two-parameter probability weighting function where one of these parameters depends on the time at which a prospect is resolved. The time-dependent parameter is responsible for the curvature of the probability weighting function and is regarded as an index of (in)sensitivity towards changes in probabilities. We provide conditions that characterize increased sensitivity towards more distant probabilities; this can account for the observed relatively less risk aversion towards delayed prospects. In our framework, the discount function is unrestricted, such that the model is compatible with empirical findings of non-constant discounting. In a simple application to bargaining we illustrate when it is advantageous for an individual to advance or delay the bargaining resolution time if an opponent displays increased sensitivity towards probability changes with delay.

Citation

Pan, J., Webb, C., & Zank, H. (2019). Delayed Probabilistic Risk Attitude: A Parametric Approach. Theory and Decision, 87(2), 201-232. https://doi.org/10.1007/s11238-019-09712-9

• Journal Article Type: Article
• Acceptance Date: Jun 6, 2019
• Online Publication Date: Jun 21, 2019
• Publication Date: Sep 30, 2019
• Deposit Date: Jun 24, 2019
• Publicly Available Date: Jul 3, 2019
• Journal: Theory and Decision
• Print ISSN: 0040-5833
• Electronic ISSN: 1573-7187
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 87
• Issue: 2
• Pages: 201-232
• DOI: https://doi.org/10.1007/s11238-019-09712-9
• Public URL: https://durham-repository.worktribe.com/output/1298877