Reciprocal Specific Relative Entropy between Continuous Martingales
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910023827849216 |
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| author | Backhoff, Julio Zhang, Xin |
| author_facet | Backhoff, Julio Zhang, Xin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14776 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reciprocal Specific Relative Entropy between Continuous Martingales Backhoff, Julio Zhang, Xin Optimization and Control Probability 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. |
| title | Reciprocal Specific Relative Entropy between Continuous Martingales |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2602.14776 |