Reciprocal Specific Relative Entropy between Continuous Martingales
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Backhoff, Julio, Zhang, Xin
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7129620833
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