Journal
MANAGEMENT SCIENCE
Volume 57, Issue 2, Pages 315-331Publisher
INFORMS
DOI: 10.1287/mnsc.1100.1269
Keywords
portfolio choice; single period; cumulative prospect theory; reference point; loss aversion; S-shaped utility function; probability weighting; well-posedness
Funding
- Columbia University
- RGC Earmarked [CUHK418605]
- University of Oxford
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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.
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