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Forward rank‐dependent performance criteria : time‐consistent investment under probability distortion
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He, Xue Dong, Strub, Moris S. and Zariphopoulou, Thaleia (2021) Forward rank‐dependent performance criteria : time‐consistent investment under probability distortion. Mathematical Finance, 31 (2). pp. 683-721. doi:10.1111/mafi.12298 ISSN 0960-1627.
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Official URL: http://dx.doi.org/10.1111/mafi.12298
Abstract
We introduce the concept of forward rank-dependent performance criteria, extending the original notion to forward criteria that incorporate probability distortions. A fundamental challenge is how to reconcile the time-consistent nature of forward performance criteria with the time-inconsistency stemming from probability distortions. For this, we first propose two distinct definitions, one based on the preservation of performance value and the other on the time-consistency of policies and, in turn, establish their equivalence. We then fully characterize the viable class of probability distortion processes and provide the following dichotomy: it is either the case that the probability distortions are degenerate in the sense that the investor would never invest in the risky assets, or the marginal probability distortion equals to a normalized power of the quantile function of the pricing kernel. We also characterize the optimal wealth process, whose structure motivates the introduction of a new, ‘distorted’ measure and a related market. We then build a striking correspondence between the forward rank-dependent criteria in the original market and forward criteria without probability distortions in the auxiliary market. This connection also provides a direct construction method for forward rank-dependent criteria. Finally, our results on forward rank-dependent performance criteria motivate us to revisit the classical (backward) setting. We follow the so-called dynamic utility approach and derive conditions for existence and a construction of dynamic rank-dependent utility processes.
| Item Type: | Journal Article | ||||||||
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| Divisions: | Faculty of Social Sciences > Warwick Business School | ||||||||
| Journal or Publication Title: | Mathematical Finance | ||||||||
| Publisher: | Wiley | ||||||||
| ISSN: | 0960-1627 | ||||||||
| Official Date: | April 2021 | ||||||||
| Dates: |
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| Volume: | 31 | ||||||||
| Number: | 2 | ||||||||
| Page Range: | pp. 683-721 | ||||||||
| DOI: | 10.1111/mafi.12298 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Access rights to Published version: | Restricted or Subscription Access |
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