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We model the market maker's problem as a stochastic optimal control problem on a filtered probability space, where the controls are adaptive bid-ask spreads and inventory hedging decisions across two exchanges. Our contributions include: (i) a PnL decomposition theorem separating revenue into spread income, adverse selection loss, inventory carrying cost, hedging friction, and funding rate exposure; (ii) the Hamilton-Jacobi-Bellman equation for the joint spread-inventory-hedging control problem under CARA utility with a verification theorem; (iii) High-APY Regime Theorems characterizing profitable regions via five dimensionless parameters, culminating in a Master APY Formula; (iv) analysis of zero-fee economics on decentralized perpetual exchanges with optimal entry-exit thresholds; (v) optimal cross-exchange hedging p","title":"Optimal Adaptive Market Making: A Theoretical Framework for High-Yield Liquidity Provision in Perpetual Futures Markets","url":"https://arxiv.org/abs/2607.11888","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.11888v1 Announce Type: new \nAbstract: We develop a rigorous theoretical framework for optimal market making in perpetual futures markets with zero maker fees. We model the market maker's problem as a stochastic optimal control problem on a filtered probability space, where the controls are adaptive bid-ask spreads and inventory hedging decisions across two exchanges. Our contributions include: (i) a PnL decomposition theorem separating revenue into spread income, adverse selection loss, inventory carrying cost, hedging friction, and funding rate exposure; (ii) the Hamilton-Jacobi-Bellman equation for the joint spread-inventory-hedging control problem under CARA utility with a verification theorem; (iii) High-APY Regime Theorems characterizing profitable regions via five dimensionless parameters, culminating in a Master APY Formula; (iv) analysis of zero-fee economics on decentralized perpetual exchanges with optimal entry-exit thresholds; (v) optimal cross-exchange hedging p","title":"Optimal Adaptive Market Making: A Theoretical Framework for High-Yield Liquidity Provision in Perpetual Futures Markets","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-15T04:44:03Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.11888"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:1b0bf0d8676d10ce8c2f2f27ade000605310bfa00f4c375bbe91c04972fb25de2fe68fbc11fcfe1b84b4f876c4cb1d4528dc8809a7837c916a7f5ba3cf271000","signer":"crovia.substrate","subject":{"observed_at":"2026-07-15T04:44:03Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.11888"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"4541b0936ae10da9bc0d1e96f6bb44a3f61a5a154fde4d9144b9ee2513235ec1","leaf_index":316356,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"632f4d0d15eba478ba002e29f6e241803bbe88e69d35a76d54f2c1171d92923b","side":"right"},{"sibling":"75a12d3e5187f6fdb5cc8985a96ab3c70dd2cc17cc6cb854b277c16c0580bea6","side":"right"},{"sibling":"e8e3f88dbcd9df6b71b0ecaa6fab657ed53efb0885cbf300572c32c266415bbe","side":"left"},{"sibling":"68e33fda57530f4c1760eaeb8a2a4046b8e55562f4a32bd05d78c608f1af213f","side":"right"},{"sibling":"1ee6a51338f7f37f1b61485abb18de300063fa8a9a4b17dc33d9338da76b64a8","side":"right"},{"sibling":"2e6e43c7a0f7f6499621f0f438d8189318d67ceb374377041278440cc38473f6","side":"right"},{"sibling":"8dc6b151fc86f1b43f490c2263dd78189a9778cebe1755f2bcd01eb2c6239831","side":"left"},{"sibling":"9a178a31a5d97bdb1bf054b31ec2fcc6cf9b633c6d3f460e934451a35bac9c25","side":"left"},{"sibling":"31b0ff6eae164fcff8882af2b581471a08fffa2373505e1f33f01e361c94a42f","side":"left"},{"sibling":"e1ebad13fafe4a9a53c35e1f19fa67a19c940f70a4211d1fab42cf49be486a3c","side":"left"},{"sibling":"c265283bb70fb86740bdfa059cfe36cfea4a5f903b841822b2954814237de972","side":"right"},{"sibling":"0cb62c0ada57a2406a6bcb100889d3e8b29a15efeed07adaff5bb90a5e80612a","side":"right"},{"sibling":"0b69289b25462ddd6166f6f49004cfc8ada0ab4f10adafe188347817bdd46e37","side":"left"},{"sibling":"1418b281cd985b5ed411ef25f2017a1826cc14919b6fad3934e6ceeec693699b","side":"right"},{"sibling":"f302542c38ba7c3aab7c9280dd60259ecec777dca6e6f71b6f0729b0b8791b72","side":"left"},{"sibling":"d8b9143917b539c543cf4448cec00131f8b807bd8004979c54ebe09798748c66","side":"left"},{"sibling":"abe4a8c706e530484d1e96a8988cb09eab85928b2050985500ab289753fe3eec","side":"right"},{"sibling":"f436dccf82aa2c1eb7bfa3eb84316e116aaf64dc55cd9592597118f6cb0648f6","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":316730,"merkle_root":"a8e6e5be81ea6f5b5f2227422459bf39455fe9f0b6602b4d1ce6977dbfd78bc7","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260715T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-15T05:38:24Z","sig_algorithm":"ed25519","signature":"df1678d268b5a07413e2ca6e748c3f40b6cfedea930a18d843489a4ab513da791bf0a886caab1b918d0989f8ebaaf3d0035ca2aa777913b1ad29979f1deb9a0c","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_80e065d6f10eacde682874df3b575b2eac32c5228388c12291101004624184a3"}}