{
  "abstract": "Loss-versus-Rebalancing (LVR) is the dominant adverse-selection cost borne by liquidity providers on automated market makers. Under geometric Brownian motion, arbitrage profit scales with the probability of a profitable block, which vanishes as the block time $Δt \\to 0$; this is the standing argument for ever-shorter blocks. Modeling the reference price instead as a jump-diffusion, I show that the constant-product LVR rate splits into a diffusion channel carrying the known multiplier $F(γ/(σ\\sqrt{Δt}))$ and a jump channel $λV \\cdot G(γ;m,δ^2)$ carrying no $Δt$, the two interacting only through an explicitly bounded remainder. The block schedule therefore governs only one channel. For symmetric jump laws the jump channel is moreover an exact lower bound, $\\ell(Δt) \\ge λV G > 0$, so the rate does not vanish as $Δt \\to 0$, and descends slowly, as $\\sqrt{Δt}$. At Ethereum's calibrated 12-second slot the rate is 471 bp/yr against a floor of 125, so only three quarters of LP loss is schedule-addressable. At Solana's 400 ms slot the jump channel already dominates. Netting the rate against per-block consensus cost, the LP-side optimal block time is invariant in pool size and in every jump parameter $(λ,m,δ)$: jumps shift the level of LP loss but not the planner's marginal tradeoff. Volatility, the fee tier, and consensus cost set the optimum, near 8 s. However, LVR is only one input to block-time welfare, so this bounds the LP-side contribution rather than settling the design question.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30321",
  "author_total": 1,
  "authors": [
    {
      "name": "Nils Bundi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9dmkxfb9byn5m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30321",
  "fulltext_url": null,
  "id": "9dmkxfb9byn5m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30321",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "q-fin.MF"
    ],
    [
      "arxiv",
      "q-fin.TR"
    ],
    [
      "openalex",
      "1710|Blockchain Technology Applications and Security"
    ]
  ],
  "openalex": "W7204928407",
  "pdf_url": "https://arxiv.org/pdf/2608.30321",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9dmkxfb9byn5m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30321",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30321"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Optimal Block Time for AMM Liquidity Providers under Jump-Diffusion Prices",
  "title_text": "Optimal Block Time for AMM Liquidity Providers under Jump-Diffusion Prices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/9dmkxfb9byn5m",
  "venue": "arXiv",
  "versions": []
}