2019/04/02 by Xue Dong He, He, Xue Dong, Moris Simon Strub +3
Economics, Econometrics and Finance · #FOS: Economics and business #Financial Markets and Investment Strategies #Market Dynamics and Volatility #Mathematical Finance (q-fin.MF) #Monetary Policy and Economic Impact #Portfolio Management (q-fin.PM)
paper · pdf · doi:10.48550/arxiv.1904.01745
openalex publication_date 2019/04/02 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
We introduce the concept of forward rank-dependent performance processes,\nextending the original notion to forward criteria that incorporate probability\ndistortions. A fundamental challenge is how to reconcile the time-consistent\nnature of forward performance criteria with the time-inconsistency stemming\nfrom probability distortions. For this, we first propose two distinct\ndefinitions, one based on the preservation of performance value and the other\non the time-consistency of policies and, in turn, establish their equivalence.\nWe then fully characterize the viable class of probability distortion\nprocesses, providing a bifurcation-type result. Specifically, it is either the\ncase that the probability distortions are degenerate in the sense that the\ninvestor would never invest in the risky assets, or the marginal probability\ndistortion equals to a normalized power of the quantile function of the pricing\nkernel. We also characterize the optimal wealth process, whose structure\nmotivates the introduction of a new, distorted measure and a related market. We\nthen build a striking correspondence between the forward rank-dependent\ncriteria in the original market and forward criteria without probability\ndistortions in the auxiliary market. This connection also provides a direct\nconstruction method for forward rank-dependent criteria. A byproduct of our\nwork are some new results on the so-called dynamic utilities and on\ntime-inconsistent problems in the classical (backward) setting.\n