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We establish some well-posedness and comparison results for BSDEs driven byone- and multi-dimensional martingales. On the one hand, our approach islargely motivated by results and methods developed in Carbone et al. (2008) andEl Karoui and Huang (1997). On the other hand, our results are also motivatedby the recent developments in arbitrage pricing theory under funding costs andcollateralization. A new version of the comparison theorem for BSDEs driven bya multi-dimensional martingale is established and applied to the pricing andhedging BSDEs studied in Bielecki and Rutkowski (2014) and Nie and Rutkowski(2014). This allows us to obtain the existence and uniqueness results forunilateral prices and to demonstrate the existence of no-arbitrage bounds for acollateralized contract when both agents have non-negative initial endowments.

BSDEs driven by a multi-dimensional martingale and their applications to market models with funding costs