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arXiv · 2602.14776

Reciprocal Specific Relative Entropy between Continuous Martingales

Julio Backhoff·Xin Zhang
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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.

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Julio Backhoff, Xin Zhang. 2026-02-16. Reciprocal Specific Relative Entropy between Continuous Martingales. https://arxiv.org/abs/2602.14776

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