Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment
Portfolio Choice Under Cumulative Prospect Theory: An Analytical Treatment
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DOI：
10.2139/ssrn.1479580
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发表时间：
2010-09
期刊：
影响因子：
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通讯作者：
X. He;X. Zhou
中科院分区：
文献类型：
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作者：
X. He;X. Zhou
我们制定并进行了单期投资组合选择模型的分析处理，该模型具有财富参考点、具有损失厌恶的 S 形效用（价值）函数以及卡尼曼和特沃斯基累积前景理论（CPT）下的概率加权。我们引入了一种新的大额收益厌恶损失衡量标准，称为大损失厌恶度（LLAD），并表明它是模型适定性的关键决定因素。然后研究 CPT 价值函数相对于股票配置的敏感性，作为副产品，表明该函数既不是凹的也不是凸的。我们最终明确地针对参考点是无风险回报和不是无风险回报的情况（而效用函数是分段线性的）得出最佳解决方案，并且我们利用这些结果来研究最佳风险暴露相对于参考点、LLAD 和概率权重曲率的比较静态。该论文被财经熊伟接收。
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.