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URL;TYPE=URI:https://www.wpi.edu/news/calendar/events/department-mathematic
 al-sciences-financial-math-seminar-renjie-shao-florida-state-university
SUMMARY:Department of Mathematical Sciences Financial Math Seminar: Renjie 
 Shao, Florida State University
DESCRIPTION:\n\n\n      \n      \n\n\n\nTuesday, May 12th, 2026\n10:00am – 
 10:50am\nStratton Hall 202\n\nSpeaker:Renjie Shao, Florida State Universit
 y\nTitle:Polymarket: Structure and arbitrage opportunities\nAbstract: Poly
 market is a decentralized prediction market where people bet USDC on the o
 f real-world events. Legally classified in the US as a derivatives exchang
 e for binary event contracts. This talk explores the structural and mathem
 atical foundations of Polymarket. We will first examine the platform's hyb
 rid architecture, which pairs an off-chain Central Limit Order Book (CLOB)
  for zero-latency matching with on-chain Polygon smart contracts for atomi
 c settlement. We will also detail the game-theoretic mechanics of the UMA 
 Optimistic Oracle used for market resolution.The second half of the talks 
 investigates the mathematics of arbitrage within Polymarket's multi-condit
 ion markets. Because market conditions are often correlated rather than in
 dependent, inefficiencies arise. By defining valid payoff vectors to form 
 a marginal polytope, we demonstrate that arbitrage detection is fundamenta
 lly a constraint satisfaction problem. Rather than using brute-force calcu
 lation, we will discuss how to exploit these arbitrage-free boundaries usi
 ng optimization techniques.\n
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