Avellaneda-Stoikov and Cartea-Jaimungal as One Framework: A Forced Uniqueness Theorem for Inventory Market Making
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911738848346112 |
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| author | Feys, Frank M. V. |
| author_facet | Feys, Frank M. V. |
| contents | In inventory market making, the running-penalty coefficient $ϕ$ of the Cartea-Jaimungal framework and the risk-aversion parameter $γ$ of the Avellaneda-Stoikov framework are typically treated as independent free parameters, calibrated separately. We show that they are in fact not independent. A small set of axioms on the market maker's dynamic preference functional, namely cash-additivity, normalization, concavity, strong dynamic consistency, and law-invariance, forces the preference functional to be the entropic certainty-equivalent on liquidation-adjusted terminal wealth, parametrized by a single positive scalar $γ$. The Avellaneda-Stoikov framework is the unique representative of this axiom class. The Cartea-Jaimungal framework is its second-order Taylor expansion in inventory magnitude, with the running coefficient forced to $ϕ= γσ^2/2$ and (under a mild regularity condition on the liquidation cost) the terminal coefficient forced to $α= \frac{1}{2}L''(0)$. The two frameworks, typically presented as competing alternatives with the choice between them driven by tractability, are different manifestations of a single underlying object. The forced relation is invertible, $γ= 2ϕ/σ^2$, giving a consistency cross-check on independently calibrated desk parameters. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_01477 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Avellaneda-Stoikov and Cartea-Jaimungal as One Framework: A Forced Uniqueness Theorem for Inventory Market Making Feys, Frank M. V. Mathematical Finance Risk Management Trading and Market Microstructure 91B16, 91G70, 91G10, 91G80, 60H30, 93E20, 49L20 In inventory market making, the running-penalty coefficient $ϕ$ of the Cartea-Jaimungal framework and the risk-aversion parameter $γ$ of the Avellaneda-Stoikov framework are typically treated as independent free parameters, calibrated separately. We show that they are in fact not independent. A small set of axioms on the market maker's dynamic preference functional, namely cash-additivity, normalization, concavity, strong dynamic consistency, and law-invariance, forces the preference functional to be the entropic certainty-equivalent on liquidation-adjusted terminal wealth, parametrized by a single positive scalar $γ$. The Avellaneda-Stoikov framework is the unique representative of this axiom class. The Cartea-Jaimungal framework is its second-order Taylor expansion in inventory magnitude, with the running coefficient forced to $ϕ= γσ^2/2$ and (under a mild regularity condition on the liquidation cost) the terminal coefficient forced to $α= \frac{1}{2}L''(0)$. The two frameworks, typically presented as competing alternatives with the choice between them driven by tractability, are different manifestations of a single underlying object. The forced relation is invertible, $γ= 2ϕ/σ^2$, giving a consistency cross-check on independently calibrated desk parameters. |
| title | Avellaneda-Stoikov and Cartea-Jaimungal as One Framework: A Forced Uniqueness Theorem for Inventory Market Making |
| topic | Mathematical Finance Risk Management Trading and Market Microstructure 91B16, 91G70, 91G10, 91G80, 60H30, 93E20, 49L20 |
| url | https://arxiv.org/abs/2606.01477 |