Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment
对累积前景理论下的单期投资组合选择模型进行了分析性求解，引入大损失厌恶度（LLAD）这一新指标，并推导了参考点为无风险收益时的最优解，揭示了损失厌恶和概率权重对风险暴露的影响。
We formulate and carry out an analytical treatment of a single-period portfolio choice model featuring a reference point in wealth, S-shaped utility (value) functions with loss aversion, and probability weighting under Kahneman and Tversky's cumulative prospect theory (CPT). We introduce a new measure of loss aversion for large payoffs, called the large-loss aversion degree (LLAD), and show that it is a critical determinant of the well-posedness of the model. The sensitivity of the CPT value function with respect to the stock allocation is then investigated, which, as a by-product, demonstrates that this function is neither concave nor convex. We finally derive optimal solutions explicitly for the cases in which the reference point is the risk-free return and those in which it is not (while the utility function is piecewise linear), and we employ these results to investigate comparative statics of optimal risky exposures with respect to the reference point, the LLAD, and the curvature of the probability weighting. This paper was accepted by Wei Xiong, finance.