Marginal Price Optimization
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866929711878242304 |
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| author | Loesch, Stefan Richardson, Mark Bentley |
| author_facet | Loesch, Stefan Richardson, Mark Bentley |
| contents | We introduce a new framework for optimal routing and arbitrage in AMM driven markets. This framework improves on the original best-practice convex optimization by restricting the search to the boundary of the optimal space. We can parameterize this boundary using a set of prices, and a potentially very high dimensional optimization problem (2 optimization variables per curve) gets reduced to a much lower dimensional root finding problem (1 optimization variable per token, regardless of the number of the curves). Our reformulation is similar to the dual problem of a reformulation of the original convex problem. We show our reformulation of the problem is equivalent to the original formulation except in the case of infinitely concentrated liquidity, where we provide a suitable approximation. Our formulation performs far better than the original one in terms of speed - we obtain an improvement of up to 200x against Clarabel, the new CVXPY default solver - and robustness, especially on levered curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08258 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Marginal Price Optimization Loesch, Stefan Richardson, Mark Bentley Mathematical Finance We introduce a new framework for optimal routing and arbitrage in AMM driven markets. This framework improves on the original best-practice convex optimization by restricting the search to the boundary of the optimal space. We can parameterize this boundary using a set of prices, and a potentially very high dimensional optimization problem (2 optimization variables per curve) gets reduced to a much lower dimensional root finding problem (1 optimization variable per token, regardless of the number of the curves). Our reformulation is similar to the dual problem of a reformulation of the original convex problem. We show our reformulation of the problem is equivalent to the original formulation except in the case of infinitely concentrated liquidity, where we provide a suitable approximation. Our formulation performs far better than the original one in terms of speed - we obtain an improvement of up to 200x against Clarabel, the new CVXPY default solver - and robustness, especially on levered curves. |
| title | Marginal Price Optimization |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2502.08258 |