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Stochastic Maximum Principle Under Probability Distortion

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Abstract

Within the framework of the cumulative prospective theory of Kahneman and Tversky, this paper considers a continuous-time behavioral portfolio selection problem whose model includes both running and terminal terms in the objective functional. Despite the existence of S-shaped utility functions and probability distortions, a necessary condition for the optimality is derived. The results are applied to a few examples.

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Acknowledgements

We would like to than an anonymous reviewer for his/her constructive comments and suggestions which improve this paper substantially.

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Authors and Affiliations

  1. Department of Mathematics, University of Macau, Macau, China

    Qizhu Liang

  2. Department of Mathematics and SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen, 518055, China

    Jie Xiong

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  1. Qizhu Liang
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  2. Jie Xiong
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Correspondence to Jie Xiong.

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This research is supported by Macao Science and Technology Development Fund FDCT 025/2016/A1 and Southern University of Science and Technology Start up fund Y01286120 and NSFC Grants 61873325 and 11831010.

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Liang, Q., Xiong, J. Stochastic Maximum Principle Under Probability Distortion. Appl Math Optim 83, 2109–2128 (2021). https://doi.org/10.1007/s00245-019-09621-x

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