Xue Dong He

We propose a rank‐dependent portfolio choice model in continuous time that captures the role in decision making of three emotions: hope, fear, and aspirations. Hope and fear are modeled through an inverse‐S shaped probability weighting function and aspirations through a probabilistic constraint. By employing the recently developed approach of quantile formulation, we solve the portfolio choice problem both thoroughly and analytically. These solutions motivate us to introduce a fear index, a hope index, and a lottery‐likeness index to quantify the impacts of three emotions, respectively, on investment behavior. We find that a sufficiently high level of fear endogenously necessitates portfolio insurance. On the other hand, hope is reflected in the agent's perspective on good states of the world: a higher level of hope causes the agent to include more scenarios under the notion of good states and leads to greater payoffs in sufficiently good states. Finally, an exceedingly high level of aspirations results in the construction of a lottery‐type payoff, indicating that the agent needs to enter into a pure gamble in order to achieve his goal. We also conduct numerical experiments to demonstrate our findings.

We consider an optimal insurance design problem for an individual whose preferences are dictated by the rank‐dependent expected utility (RDEU) theory with a concave utility function and an inverse‐S shaped probability distortion function. This type of RDEU is known to describe human behavior better than the classical expected utility. By applying the technique of quantile formulation, we solve the problem explicitly. We show that the optimal contract not only insures large losses above a deductible but also insures small losses fully. This is consistent, for instance, with the demand for warranties. Finally, we compare our results, analytically and numerically, both to those in the expected utility framework and to cases in which the distortion function is convex or concave.