A Parametric Contextual Online Learning Theory of Brokerage
This work addresses the challenge of efficient brokerage in sequential trading scenarios, though it appears incremental as it builds on existing online learning frameworks.
The paper tackles the problem of brokerage between traders in an online learning setting, where a broker uses contextual information to set prices, and achieves optimal theoretical regret guarantees under standard assumptions.
We study the role of contextual information in the online learning problem of brokerage between traders. In this sequential problem, at each time step, two traders arrive with secret valuations about an asset they wish to trade. The learner (a broker) suggests a trading (or brokerage) price based on contextual data about the asset and the market conditions. Then, the traders reveal their willingness to buy or sell based on whether their valuations are higher or lower than the brokerage price. A trade occurs if one of the two traders decides to buy and the other to sell, i.e., if the broker's proposed price falls between the smallest and the largest of their two valuations. We design algorithms for this problem and prove optimal theoretical regret guarantees under various standard assumptions.