A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Optimal pricing strategy for unknown valuation models with noisy feedback.
problem Minimizing regret in dynamic pricing with unknown valuation functions and noisy feedback.
method Proposes a minimax-optimal algorithm using discretization and data partitioning to handle unknown noise distribution and Lipschitz continuity of valuation functions.
result Achieves minimax-optimal regret bound matching the theoretical lower bound up to logarithmic factors.
Study optimal pricing for dynamic contexts with unknown demand parameters.
problem Optimal pricing in dynamic contexts with unknown demand parameters.
method Develops a pilot-corrected layered decision-partitioning policy combining directional pilot estimation, local polynomial learning, predictable data assignment, and global action elimination.
result Achieves minimax optimal performance up to logarithmic factors.
Study convolution of invariant valuations on Lie groups.
problem Understanding convolution of valuations on Lie groups.
method Explicit formula for left-invariant valuations, showing existence of smooth bi-invariant valuations, defining convolution on arbitrary Lie groups.
result Unified convolution operations on Lie groups.
We prove new kinematic formulas for tensor valuations and simplify previously known Crofton formulas by using the recently developed algebraic theory of translation invariant valuations. The heart of the paper is the computation of the Alesker-Fourier transform on the large class of spherical valuations, which is achie…
The classification of continuous, translation invariant Minkowski valuations which are contravariant (or covariant) with respect to the complex special linear group is established in a 2-dimensional complex vector space. Every such valuation is given by the sum of a valuation of degree of homogeneity 1 and 3. In dimens…
Classifies SL(n) covariant matrix-valued valuations on Lp-spaces.
problem Classifying SL(n) covariant matrix-valued valuations on Lp-spaces.
method Established a complete classification for continuous and SL(n) covariant matrix-valued valuations on Lp(Rn,|x|2dx), eliminating matrix symmetry assumption.
result Unique characterization of such valuations by the moment matrix in n>2, rotation matrix in 2D.
We study the properties of the multiplicative structure on valuations on convex sets. We prove a new version of the hard Lefschetz theorem for even translation invariant continuous valuations, and discuss related problems of integral geometry. Then we formulate a conjectural analogue of this result for odd valuations.
We give an explicit classification of translation-invariant, Lorentz-invariant continuous valuations on convex sets. We also classify the Lorentz-invariant even generalized valuations.
A description of continuous rigid motion compatible Minkowski valuations is established. As an application, we present a Brunn-Minkowski type inequality for intrinsic volumes of these valuations.
Enhances data valuation by integrating global and local statistical properties.
problem Insufficient consideration of global and local statistical properties in data valuation methods.
method Proposes a method that fuses global and local statistical properties into regularization terms for Shapley value estimation and dynamic data valuation.
result Demonstrates improved performance and efficiency of data valuation methods through integration of global and local statistical properties.
We study the space of generalized translation invariant valuations on a finite-dimensional vector space and construct a partial convolution which extends the convolution of smooth translation invariant valuations. Our main theorem is that McMullen's polytope algebra is a subalgebra of the (partial) convolution algebra …
A complete classification of all continuous GL(n) contravariant Minkowski valuations is established. As an application we present a family of sharp isoperimetric inequalities for such valuations which generalize the classical Petty projection inequality.