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Adaptive Market Making with Inventory Constraints via Online Learning
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Proposes hard- and soft-inventory-constrained fixed-spread market-making reference strategies and runs MW and FPL online learning over them, proving sublinear regret with state-dependent gain bounds and evaluating on CSI 500 tick data.
Problem
Market making under inventory risk within a model-free online learning framework, where existing no-regret market-making strategies focus on PnL and can accumulate large inventory during trends.
Approach
Builds two classes of inventory-controlled fixed-spread reference strategies (hard window-limit and soft linear inventory-skew) so that online learning over them keeps inventory bounded; the per-period gain depends on inventory, so regret analysis bounds the gain difference between reference strategies.
Key results
- Realized average regret per period is below the theoretical bound for all stock paths and parameter settings (Gmin positive for ASMW and ASFPL on both constraint classes, Table 2).
- ASMW on hard- and soft-constraint strategies achieves higher Sharpe ratios (e.g., 0.21-0.24 hard, 0.15-0.23 soft) than the non-constraint ASMW baseline (0.13), and lower final inventory (H about 5.5-18 vs 38.4).
- In uptrend and downtrend subsamples, constrained adaptive strategies make profits while non-constraint strategies make losses.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add hard- or soft-inventory constraints to ASMW | ASMW market-making strategy · CSI 500 stock paths, full sample | Sharp ratio: 0.13; constrained values 0.15 to 0.24 | Helped |
| Add hard- or soft-inventory constraints to ASMW | ASMW market-making strategy · CSI 500 stock paths, full sample | mean final absolute inventory: 38.42; hard R=10: 5.52; soft γ=0.5δ: 5.71 | Helped |
| Add hard- or soft-inventory constraints to ASFPL | ASFPL market-making strategy · CSI 500 stock paths, full sample | Sharp ratio: 0.08; constrained values -0.17 to -0.04 | Hurt |
| Add hard- or soft-inventory constraints to ASFPL | ASFPL market-making strategy · CSI 500 stock paths, full sample | mean final absolute inventory: 46.32; hard R=10: 5.33; soft γ=0.5δ: 6.01 | Helped |
| Increase hard inventory limit from R=10 to R=50 (ablation) | ASMW hard-constraint strategy · CSI 500 stock paths, full sample | mean final absolute inventory: 5.52 -> 18.25 | Hurt |
| Increase soft risk-aversion coefficient from γ=0.1δ to γ=0.5δ (ablation) | ASMW soft-constraint strategy · CSI 500 stock paths, full sample | mean final absolute inventory: 12.15 -> 5.71 | Helped |
| Increase soft risk-aversion coefficient from γ=0.1δ to γ=0.5δ (ablation) | ASMW soft-constraint strategy · CSI 500 stock paths, full sample | Sharp ratio: 0.23 -> 0.15 | Hurt |
| Increase soft risk-aversion coefficient from γ=0.1δ to γ=0.5δ (ablation) | ASFPL soft-constraint strategy · CSI 500 stock paths, full sample | mean final absolute inventory: 13.49 -> 6.01 | Helped |
| Increase soft risk-aversion coefficient from γ=0.1δ to γ=0.5δ (ablation) | ASFPL soft-constraint strategy · CSI 500 stock paths, full sample | Sharp ratio: -0.06 -> -0.17 | Hurt |
Surprising findings
- ASFPL on all constraint and non-constraint settings has negative average gain per period in the full sample, while ASMW is profitable.
- Inventory control reduces gain in no-trend paths, which dominate the sample.
Limitations
- Assumes no transaction costs, perfectly divisible stock, and exogenous prices, which the authors acknowledge are unrealistic.
- Only the spread parameter is learned; bid and ask distances are not learned independently.
- Soft-constraint analysis restricted to 0 < gamma <= tick size; large gamma causes liquidation losses in non-trend markets.
Experimental setup
Datasets: CSI 500 component stocks tick-by-tick data, December 2022
Benchmarks: CSI 500 tick-by-tick stock price paths (10,882 paths)
Metrics: average gain per period standard deviation of gain Sharpe ratio absolute final inventory regret vs. theoretical bound (Gmin)
Baselines: Non-constraint strategies (Abernethy and Kale 2013) ASFPL ASMW
Builds on: Abernethy and Kale 2013 no-regret market making Multiplicative weights Follow-the-perturbed-leader Das 2005
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