We are grateful for comments from seminar and conference participants at the Chinese University of Hong Kong, Columbia University, Tongji University, the University of St. Gallen, Risk and Stochastics Day 2010 at the London School of Economics and Political Science, the 2010 Workshop on Stochastics, Control and Finance at Imperial College, the Sixth World Congress of the Bachelier Finance Society in Toronto, the Sixth Oxford-Princeton Workshop on Mathematical Finance at the University of Oxford, the 2011 SIAM Conference on Control and Its Applications in Baltimore, the 2011 Workshop of the Sino-French Summer School in Stochastic Modeling and Applications in Beijing, the 2011 HKU-HKUST-Stanford Conference in Quantitative Finance in Hong Kong, the Seventh World Congress of the Bachelier Finance Society in Sydney, the St. Gallen Workshop in Quantitative Behavioral Finance, the First Asian Quantitative Finance Conference in Singapore, and the Twelfth Winter School on Mathematical Finance in Lunteren. We thank an anonymous referee for extremely detailed and constructive comments. The first author acknowledges financial support from a start-up fund at Columbia University, and the second author acknowledges financial support from a start-up fund at the University of Oxford, research funds from the Nomura Centre for Mathematical Finance and from the Oxford–Man Institute of Quantitative Finance, and GRF Grant #CUHK419511.
HOPE, FEAR, AND ASPIRATIONS
Article first published online: 18 JUN 2013
© 2013 Wiley Periodicals, Inc.
Volume 26, Issue 1, pages 3–50, January 2016
How to Cite
He, X. D. and Zhou, X. Y. (2016), HOPE, FEAR, AND ASPIRATIONS. Mathematical Finance, 26: 3–50. doi: 10.1111/mafi.12044
- Issue published online: 11 JAN 2016
- Article first published online: 18 JUN 2013
- Manuscript Revised: MAR 2013
- Manuscript Received: JUL 2012
- portfolio choice;
- continuous time;
- rank-dependent utility;
- probability weighting;
- SP/A theory;
- quantile formulation;
- portfolio insurance
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.