Cartea-Jaimungal Market Making

The classic Avellaneda-Stoikov market-making model sets a dealer's bid and ask quotes by balancing inventory risk (how much the dealer wants to hold) against the probability of getting filled, but it treats incoming order flow as a simple random arrival process, without asking whether an incoming order carries information about where the price is about to move. The Cartea-Jaimungal framework extends this by explicitly modeling order flow as informative — some incoming market orders are placed by traders who know something, and getting run over by that flow (adverse selection) is a distinct risk from simply holding unwanted inventory.

Concretely, the framework lets the arrival intensity of buy and sell market orders, and the price's own drift, depend on recent order flow imbalance — if sells have been hitting the bid persistently, that's read as a signal the price is more likely to keep falling, not just noise to be absorbed. The dealer's optimal quotes then skew not only to manage inventory (as in Avellaneda-Stoikov) but also to defensively react to that informational signal, quoting a wider or more skewed spread when recent flow looks toxic.

This matters in practice because a market maker who ignores order-flow information will systematically get picked off during informed trading bursts (like ahead of news or in a fast-moving trend), accumulating losing inventory exactly when informed traders are most active — the Cartea-Jaimungal adjustment is a mathematical way of building "read the flow, then quote defensively" into the same optimization that already handles inventory risk.