Tuesday, March 22, 2016. 12:00PM. NSH 1507.

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Christian Kroer - Arbitrage-free Combinatorial Market Making via Integer Programming

We present a new combinatorial market maker that operates arbitrage-free combinatorial markets specified by integer programs. The problem of arbitrage-free pricing, while maintaining a bound on the subsidy provided by the market maker, is #P-hard in the worst-case. However, we posit that the typical case might be amenable to modern integer programming (IP) solvers. At the crux of our method is the Frank-Wolfe (conditional gradient) algorithm which is used to implement a Bregman projection aligned with the market maker's cost function, using an IP solver as an oracle. We demonstrate the tractability and improved accuracy of our approach on real-world prediction market data from combinatorial bets placed on the 2010 NCAA Men's Division I Basketball Tournament, where the outcome space is of the size 2^63. To our knowledge, this is the first implementation and empirical evaluation of an arbitrage-free market on this scale.

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