Yang, Qiulin and Busby, Jerry (2019) The choice-theoretic characterizations of risk changes and risk attitudes in cumulative prospect theory : a stochastic dominance approach. PhD thesis, Lancaster University.
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Abstract
Stochastic dominance provides an effective tool to characterize individuals’ risk attitudes in decision making under risk by comparing risky prospects. The emergence of the cumulative prospect theory (CPT), developed by Kahneman and Tversky (1979) and Tversky and Kahneman (1992), provides a prominent alternative to the expected utility theory. This thesis aims to provide a choice-theoretic characterization for risk changes and risk attitudes under CPT using a stochastic dominance approach. This thesis identifies a set of stochastic dominance conditions to generalize the notions of increase in risk, strong risk aversion, downside risk and downside risk aversion to accommodate risk aversion, risk seeking and downside risk aversion preferences in the CPT paradigm. This study further investigates risk measures implied by risky choice behaviour of CPT decision makers. This thesis also extends the analyses to general reference point and inverse S-shaped value functions. The stochastic dominance conditions identified in this thesis provide an approach for risk preference elicitation in the paradigm of CPT without prior knowledge on the shape of value functions or probability weighting functions, which complements to existing risk preference elicitation approaches. Consequently, the equivalence of risk measures and stochastic dominance conditions enables risk preference elicitation through pairwise comparisons of risky prospects. The implications of this work in experimental studies and optimal decision problems (e.g. portfolio choice) shed new light into the application of CPT.