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HOPE, FEAR, AND ASPIRATIONS
Author(s) -
He Xue Dong,
Zhou Xun Yu
Publication year - 2016
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12044
Subject(s) - portfolio , lottery , probabilistic logic , stochastic game , portfolio insurance , constraint (computer aided design) , economics , index (typography) , weighting , mathematical economics , project portfolio management , function (biology) , econometrics , microeconomics , computer science , mathematics , portfolio optimization , artificial intelligence , replicating portfolio , financial economics , medicine , geometry , management , evolutionary biology , project management , biology , world wide web , radiology
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.