Avellaneda-Stoikov 2008
“High-frequency trading in a limit order book” by Marco Avellaneda and Sasha Stoikov (NYU), Quantitative Finance 8(3):217-224, 2008, is the canonical quantitative formulation of Market Making as a stochastic optimal-control problem. A dealer posts bid/ask limit orders around a driftless Brownian-motion mid-price and maximises terminal exponential (CARA) utility of P&L; the closed-form solution skews quotes around an inventory-dependent reservation price r(s,q,t) = s − q·γ·σ²·(T−t) and sets a spread with an inventory-risk term and an order-arrival term. It appears in this vault as the model-based baseline for the trading Markov Decision Process Trading Model — a fully specified MDP solved by dynamic programming — and as the framework that reinforcement-learning market makers such as Lalor Swishchuk 2025 are benchmarked against and argue against.
Its key limitation is the Poisson order-arrival assumption (λ(δ) = A·exp(−k·δ)): arrivals are memoryless and independent of the price process, which real microstructure rejects in favour of self-exciting Hawkes Process dynamics. The paper is a simulation study: it reports lower inventory-risk variance than a naive symmetric strategy — a risk-management result — not real-data, cost-adjusted, out-of-sample profitability, so its profitability evidence grade is inconclusive.
Connections
- Market Making — proposes_model, 2008, source: https://people.orie.cornell.edu/sfs33/LimitOrderBook.pdf
- Markov Decision Process Trading Model — proposes_model (model-based MDP solved by dynamic programming), source: https://people.orie.cornell.edu/sfs33/LimitOrderBook.pdf
- Limit Order Book — trades_market, source: https://people.orie.cornell.edu/sfs33/LimitOrderBook.pdf
- Hawkes Process — contradicts (Poisson arrivals vs self-exciting reality), source: https://people.orie.cornell.edu/sfs33/LimitOrderBook.pdf
- Lalor Swishchuk 2025 — compares_benchmark (RL study argues against this stochastic-control lineage), source: https://arxiv.org/html/2410.14504v2
- Almgren Chriss 2000 — relates (sibling stochastic-control formulation for execution), source: https://people.orie.cornell.edu/sfs33/LimitOrderBook.pdf