Reciprocal Specific Relative Entropy between Continuous Martingales
Optimization and Control
2026-02-17 v1 Probability
Abstract
We introduce a novel notion of divergence between continuous martingales; the reciprocal specific relative entropy. First, we motivate this definition from multiple perspectives. Thereafter, we solve the reciprocal specific relative entropy minimization problem over the set of win-martingales (used as models for prediction markets Aldous (2013)). Surprisingly, we show that the optimizer is the renowned neutral Wright-Fisher diffusion. We also justify that this diffusion is in a sense the most salient win-martingale, since it is uniquely selected when we suitably perturb the degenerate martingale optimal transport problem of variance minimization.
Cite
@article{arxiv.2602.14776,
title = {Reciprocal Specific Relative Entropy between Continuous Martingales},
author = {Julio Backhoff and Xin Zhang},
journal= {arXiv preprint arXiv:2602.14776},
year = {2026}
}