Brokerage

A Parametric Contextual Online Learning Theory of Brokerage ArXiv ID: 2407.01566 “View on arXiv” Authors: Unknown Abstract 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. ...

Trading Volume Maximization with Online Learning ArXiv ID: 2405.13102 “View on arXiv” Authors: Unknown Abstract We explore brokerage between traders in an online learning framework. At any round $t$, two traders meet to exchange an asset, provided the exchange is mutually beneficial. The broker proposes a trading price, and each trader tries to sell their asset or buy the asset from the other party, depending on whether the price is higher or lower than their private valuations. A trade happens if one trader is willing to sell and the other is willing to buy at the proposed price. Previous work provided guidance to a broker aiming at enhancing traders’ total earnings by maximizing the gain from trade, defined as the sum of the traders’ net utilities after each interaction. In contrast, we investigate how the broker should behave to maximize the trading volume, i.e., the total number of trades. We model the traders’ valuations as an i.i.d. process with an unknown distribution. If the traders’ valuations are revealed after each interaction (full-feedback), and the traders’ valuations cumulative distribution function (cdf) is continuous, we provide an algorithm achieving logarithmic regret and show its optimality up to constant factors. If only their willingness to sell or buy at the proposed price is revealed after each interaction ($2$-bit feedback), we provide an algorithm achieving poly-logarithmic regret when the traders’ valuations cdf is Lipschitz and show that this rate is near-optimal. We complement our results by analyzing the implications of dropping the regularity assumptions on the unknown traders’ valuations cdf. If we drop the continuous cdf assumption, the regret rate degrades to $Θ(\sqrt{“T”})$ in the full-feedback case, where $T$ is the time horizon. If we drop the Lipschitz cdf assumption, learning becomes impossible in the $2$-bit feedback case. ...