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math.MG2026
Preimage Regions of Symmetric Separable Maps on the Simplex: Convexity and Barycentric Star-Shapedness
Jilong Xu, Xiaojun Cui
We study preimage regions on the open probability simplex associated with symmetric separable functionally generated maps. The problem is a finite-dimensional geometric question ab…
math.OC2026
The Geometry of Admissible Short Selling in Discrete-Time Stochastic Portfolio Theory
Jilong Xu, Xiaojun Cui
While discrete-time Stochastic Portfolio Theory (SPT) provides a robust framework for market analysis, existing work on functional generation has predominantly focused on long-only…