Multi-Task Dynamic Pricing in Credit Market with Contextual Information

We study the dynamic pricing problem faced by a broker seeking to learn prices for a large number of credit market securities, such as corporate bonds, government bonds, loans, and other credit-related securities. A major challenge in pricing these securities stems from their infrequent trading and the lack of transparency in over-the-counter (OTC) markets, which leads to insufficient data for individual pricing. Nevertheless, many securities share structural similarities that can be exploited. Moreover, brokers often place small "probing" orders to infer competitors' pricing behavior. Leveraging these insights, we propose a multi-task dynamic pricing framework that leverages the shared structure across securities to enhance pricing accuracy. In the OTC market, a broker wins a quote by offering a more competitive price than rivals. The broker's goal is to learn winning prices while minimizing expected regret against a clairvoyant benchmark. We model each security using a $d$-dimensional feature vector and assume a linear contextual model for the competitor's pricing of the yield, with parameters unknown a priori. We propose the Two-Stage Multi-Task (TSMT) algorithm: first, an unregularized MLE over pooled data to obtain a coarse parameter estimate; second, a regularized MLE on individual securities to refine the parameters. We show that the TSMT achieves a regret bounded by $\tilde{O} ( \delta_{\max} \sqrt{T M d} + M d ) $, outperforming both fully individual and fully pooled baselines, where $M$ is the number of securities and $\delta_{\max}$ quantifies their heterogeneity.