Essays on comparative statics for choice under risk and ambiguity

  • Tian LI

Student thesis: PhD Thesis (Lingnan)


This dissertation contains three essays on choice under risk and ambiguity. In the first essay, we investigate the effects of changes in ambiguity aversion in a recursive smooth ambiguity aversion model. Wang and Li [Wang J. and Li J. (2020) Comparative Ambiguity Aversion in Intertemporal Decisions. J. Risk Insurance 87(1): 195-212] explore this topic under the assumption that the current payment increases the future expected utility conditional on any given ambiguity parameter, which limits the applicability of their conclusions. In this paper, we report that this assumption can be relaxed. We further show that, the comparative ambiguity aversion result provides broader applicability for fundamental economics decision-making problems, e.g., investment and self-protection with decision externalities.

In the second essay, we investigate the comparative statics on the choice of a cutoff point in a screening test program. By considering interdependence between wealth and health, this study illustrates the importance of higher-order bivariate preferences on the choice of an optimal screening test schedule. We show that when background risk is introduced to the wealth dimension, the preferences, temperance in wealth, cross temperance in health and cross temperance, lead to a more aggressive choice, indicated by higher sensitivity of the test program. We further show that increasing the correlation between a health-related background risk and the basic two-dimensional risk increases the decision makers' inclination toward higher sensitivity tests if they show correlation aversion and risk aversion. Last, we demonstrate comparative choice on test characteristics when the second-period wealth experiences a mean-preserving spread.

In the third essay, we develop measures for three types of risk that exert a pair of risk tradeoffs on initial random wealth. The three measures are independent of the agent accepting the risk and are monotone with respect to specific stochastic dominance orders. We show that the duality axiom could characterize the risk measures. We then apply the risk measures to three other risk tradeoffs that involve three changes in risk. We show that the risk measures could infer the choices for two agents on two outcome lotteries. In addition, we augment the literature on separation theorem by providing decomposition for the risk tradeoffs defined in this paper. Finally, we briefly discuss the implications of the duality axioms in a one-period self-protection model.
Date of Award29 Jun 2023
Original languageEnglish
Awarding Institution
  • Lingnan University
SupervisorJingyuan LI (Supervisor) & Tao SUN (Co-supervisor)

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