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.

翻译：本文提出了一种在期望约束下进行密度估计的新框架。该框架在约束条件下最小化估计密度与先验分布之间的Wasserstein距离，约束条件要求一组函数的期望值达到或超过给定阈值。该框架进一步推广至包含正则化不等式，以缓解目标度量中的伪影问题。针对非光滑约束，本文开发了一种类退火算法，并通过金融领域的合成数据与概念验证实例证明了其有效性。