🤖 AI Summary
This study addresses the problem of probability density estimation under prescribed expectation constraints. The authors propose an optimization framework based on the Wasserstein distance, which minimizes the discrepancy between the estimated density and a prior distribution while incorporating a regularization term to suppress artifacts in the target measure. The key innovation lies in the novel integration of optimal transport theory with expectation-constrained density estimation, alongside the development of an annealing algorithm capable of handling nonsmooth constraints. Experimental results on both synthetic data and real-world financial applications demonstrate the method’s effectiveness: the resulting density estimates rigorously satisfy the imposed constraints and exhibit strong structural plausibility.
📝 Abstract
A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of functions adopts or exceeds given values. The framework is generalized to include regularization inequalities to mitigate the artifacts in the target measure. An annealing-like algorithm is developed to address non-smooth constraints, with its effectiveness demonstrated through both synthetic and proof-of-concept real world examples in finance.