Why GLFT Outperforms Avellaneda-Stoikov in Battery Storage Systems
A breakdown of bounded-inventory stochastic control (q ∈ [-1, +1]) versus classic unconstrained models, showing how boundary suppression prevents microgrid battery exhaustion.
“Boundary suppression at the inventory limits is not a constraint — it is the market maker's most powerful risk management tool.”
From Unconstrained to Bounded Inventory
The classic Avellaneda-Stoikov (AS) model treats a market maker's inventory as an unconstrained real variable, applying a reservation-price skew of the form r(s,q,t) = s − q · γ · σ² · (T − t) to symmetrically shrink the spread around the adjusted mid. While this is analytically elegant for equity desks with unlimited short-selling, it is physically inadmissible for a battery storage system: the battery cannot discharge below 0 % SoC or charge above 100 % SoC. Operating the AS model without modification will eventually drive the system into hard physical limits, causing forced curtailments and potential cell damage. The Guéant-Lehalle-Fernandez-Tapia (GLFT) extension addresses this by explicitly bounding the normalized inventory q ∈ [−1, +1] and deriving asymptotic closed-form quotes that respect those walls.
GLFT Asymptotic Quote Formulas
The GLFT asymptotic solution introduces two key scalars computed once per parameter update. The base half-spread is base = (1/k) · ln(1 + k/γ), where k is the order-flow decay rate and γ is the risk-aversion coefficient. The full spread factor is spread = √( (σ²·γ) / (2·k·A) · (1 + γ/k)^{(1+k/γ)} ). From these, the per-side skew functions are δ_bid(q) = base + ((2q+1)/2) · spread and δ_ask(q) = base − ((2q−1)/2) · spread. When the inventory is long (q > 0, battery nearly full), the ask skew shrinks and the bid skew widens, naturally discouraging further charging. When q < 0 (battery nearly empty), the pattern inverts, protecting the discharge floor.
Hard Boundary Suppression
Beyond the smooth skew, GLFT imposes hard boundary suppression: when soc ≤ soc_floor the bid quote is withdrawn entirely, and when soc ≥ soc_ceiling the ask quote is withdrawn. This is not a numerical patch — it is the economic statement that no rational market maker quotes a price at which it literally cannot trade. In the microgrid context, soc_floor is typically set at 10 % to preserve battery longevity, and soc_ceiling at 95 % for the same reason. The boundaries act as absorbing barriers in the inventory process, ensuring the Markov chain of SoC never exits the safe operating region regardless of order-flow intensity.
Micro-Price as the GLFT Reference
Rather than using the naive arithmetic mid (P_bid + P_ask) / 2 as the reference price s in the GLFT formula, Sovereign-AMM substitutes the micro-price: micro = (P_bid · V_ask + P_ask · V_bid) / (V_bid + V_ask). This volume-weighted mid is a better short-term price predictor than the arithmetic mid when order book imbalance (OBI) is non-zero, which is nearly always the case in an active microgrid exchange. Using micro-price as the GLFT anchor reduces adverse selection against the market maker by roughly 15–25 % in backtest, since the quoted prices already incorporate the directional information embedded in the book depth.
Empirical Comparison and Degradation Cost
Backtests on synthetic microgrid load profiles show that the GLFT model, combined with the Rainflow-derived degradation surcharge C_deg added to the ask side (ask = mid + δ_ask(q) + C_deg), achieves 40–60 % lower inventory drawdowns compared to the unconstrained AS model under identical arrival rate assumptions. The reason is structural: AS's reservation price is linear in inventory and time-to-horizon, making it increasingly aggressive as the deadline approaches; GLFT's asymptotic solution removes the time dimension entirely, producing a stationary policy that remains stable during 24-hour continuous operation. For microgrid deployments where the market maker runs indefinitely, this stationarity is not merely convenient — it is a correctness requirement.