The imbalance equivalence: arrival imbalance q is absorbed exactly by a skew shift δ = (w/2)log(q/(1−q)), a widening γ, and a carry multiplier 1/(2√(q(1−q))). A flat book still skews; skew is first order in imbalance, width second.
The companion: extends the model to clustered arrivals and stochastically varying imbalance.
Dealer-inventory classics
Garman, M. B. (1976). Market microstructure. Journal of Financial Economics 3(3), 257–275. doi
The oldest imbalanced-flow dealer model: asymmetric Poisson buy and sell rates, but a single static price pair; the content is ruin, not policy.
Amihud, Y., Mendelson, H. (1980). Dealership market: market-making with inventory. Journal of Financial Economics 8(1), 31–53. doi
The closest classical antecedent in spirit: imbalanced arrivals move a preferred inventory position and monotone quotes. Structural results, no closed form.
Ho, T., Stoll, H. R. (1981). Optimal dealer pricing under transactions and return uncertainty. Journal of Financial Economics 9(1), 47–73. doi
Quotes from value-function differences. The slope half of the slope-and-convexity characterization is implicit here; the convexity half (discretionary width reveals the second difference of inventory cost) appears to be new in the core paper.
The optimal market making line
Avellaneda, M., Stoikov, S. (2008). High-frequency trading in a limit order book. Quantitative Finance 8(3), 217–224. doi
The anchor. Constant width, linear skew is reached by dropping terms, and the dropped terms are the ones needed to establish any rule regarding width.
Guéant, O., Lehalle, C.-A., Fernandez-Tapia, J. (2012). Dealing with the inventory risk: a solution to the market making problem. Mathematics and Financial Economics 7(4), 477–507. doi
The exact treatment of the Avellaneda–Stoikov problem; arrival intensities symmetric, directional asymmetry only as mid-price drift, which shifts quotes but neither widens them nor taxes carry.
Guéant, O. (2016). The Financial Mathematics of Market Liquidity. Chapman & Hall/CRC; and (2017) Optimal market making. Applied Mathematical Finance 24(2), 112–154. doi
Asymmetric intensities in generality, handled numerically. No equivalence statement, no log-odds shift, no cost multiplier.
Bergault, P., Guéant, O. (2021). Size matters for OTC market makers. Mathematical Finance 31(1), 279–322. doi; Bergault, P., Evangelista, D., Guéant, O., Vieira, D. (2021). Closed-form approximations in multi-asset market making. Applied Mathematical Finance 28(2), 101–142.
The modern generalizations: trade-size distributions, multi-asset books, dimensionality reduction. Imbalance remains numerical throughout.
Cartea, Á., Jaimungal, S., Ricci, J. (2014). Buy low, sell high. SIAM J. Financial Mathematics 5(1), 415–444. doi; Cartea, Á., Jaimungal, S. (2016). Incorporating order-flow into optimal execution. Mathematics and Financial Economics 10(3), 339–364; and Cartea, Á., Jaimungal, S., Penalva, J. (2015). Algorithmic and High-Frequency Trading. CUP.
Order-flow imbalance as a predictive signal: a different object from the stationary structural imbalance in the core paper.
Bergault, P., Guéant, O. (2023). Liquidity dynamics in RFQ markets and impact on pricing. arXiv:2309.04216
Observes numerically that flow-aware market makers skew even with no inventory. Corollary 1 of the core paper is the closed form of that observation.
RFQ markets and empirics
Hendershott, T., Madhavan, A. (2015). Click or call? Auction versus search in the over-the-counter market. Journal of Finance 70(1), 419–447. doi
Documents the sealed-bid enquiry mechanism the model takes as primitive.
Fermanian, J.-D., Guéant, O., Pu, J. (2017). The behavior of dealers and clients on the European corporate bond market. Market Microstructure and Liquidity 2(3–4), 1750004. doi
Econometrics of dealer win curves on multi-dealer-to-client platforms; empirical support for the win-curve assumption.
Butz, M., Oomen, R. (2019). Internalisation by electronic FX spot dealers. Quantitative Finance 19(1), 35–56. doi
Documents dealers skewing on flow at flat inventory: the practice Corollary 1 derives rather than assumes.
Guéant, O., Manziuk, I. (2019). Deep reinforcement learning for market making in corporate bonds. Applied Mathematical Finance 26(5), 387–452. doi
RL against the curse of dimensionality. The symmetry, read as an approximate invariance, lets a learner pool episodes across flow regimes (§6 of the core paper).
Barzykin, A., Bergault, P., Guéant, O. (2023). Algorithmic market making in dealer markets with hedging and market impact. Mathematical Finance 33(1), 41–79. doi
The current state of the RFQ control line.
The probability side
Ledermann, W., Reuter, G. E. H. (1954). Spectral theory for the differential equations of simple birth and death processes. Phil. Trans. R. Soc. A 246(914), 321–369; Karlin, S., McGregor, J. (1957). Trans. AMS 85(2), 489–546. doi
The birth–death symmetrization and its geometric mean of rates. The core paper's substitution was found independently; the provenance was noticed after the fact.
Bailey, N. T. J. (1954). A continuous time treatment of a simple queue using generating functions. JRSS B 16(2), 288–291. doi
The same substitution in the transient analysis of the simple queue.
The storage program
Weymar, F. H. (1965). The Dynamics of the World Cocoa Market. MIT PhD thesis. Distilled in literature/weymar1965.md.
Price of a storable good as a boundary-value problem: the storage relation supplies slopes of the expected-price curve, a long-run anchor supplies the level. The grounding document for the wider research program.
The wider program: what keeps optimal inventory bounded when carrying costs are tens of basis points, and whether the dealer bid–offer is the endogenous replacement for the missing carry.