Option market making with hedging-induced market impact

Etienne Chevalier; Paulin Aubert; Vathana Ly Vath

arxiv: 2511.02518 · v2 · submitted 2025-11-04 · 💱 q-fin.TR · math.PR

Option market making with hedging-induced market impact

Paulin Aubert , Etienne Chevalier , Vathana Ly Vath This is my paper

Pith reviewed 2026-05-18 01:35 UTC · model grok-4.3

classification 💱 q-fin.TR math.PR

keywords option market makingmarket impacthedgingstochastic controlCox processinventory risknumerical optimizationprice impact

0 comments

The pith

Option market makers' hedging trades generate permanent and transient impact on the underlying asset, coupling it to option order flow in a well-posed mixed control problem.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds a model in which a market maker continuously posts option quotes while occasionally executing impulsive hedges in the underlying. Option arrivals follow Cox processes whose intensities respond to the current underlying price and the posted quotes, and every hedge trade shifts the underlying price both permanently and temporarily. This feedback creates possible arbitrage or manipulation loops between the two markets. The authors prove that the resulting stochastic control problem, mixing continuous and impulse controls, is mathematically well-posed. They then compute approximate optimal policies with a numerical optimization routine to show how liquidity in the option market, inventory risk, and the cost of moving the underlying interact.

Core claim

By modeling option demand via Cox processes whose intensities depend on the underlying state and on the market maker's quoted prices, and by letting hedging trades produce both permanent and transient price impact, the authors obtain coupled dynamics for inventory and prices. They establish well-posedness of the mixed control problem that combines continuous quoting decisions with impulsive hedging actions, and they approximate optimal strategies numerically to illustrate the resulting trade-offs among option liquidity, inventory risk, and underlying impact.

What carries the argument

The mixed control problem of continuous quoting decisions together with impulsive hedging actions, driven by Cox-process order flow and subject to permanent plus transient market impact.

If this is right

Feedback between option trades and underlying impact can create arbitrage or manipulation opportunities that optimal strategies must avoid or exploit.
Optimal quoting and hedging policies must jointly manage liquidity provision in the option and the inventory risk that hedging impact amplifies.
Numerical policy optimization produces concrete strategy approximations that quantify how changes in option liquidity or impact strength alter inventory holdings and quote placement.
The well-posedness result guarantees that small changes in model parameters produce continuous changes in value functions and controls.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same mixed-control structure could be applied to market making in other assets where the maker's own trades move the reference price.
Calibrating the impact and intensity functions to observed trade data would allow direct comparison of the computed policies against real market-maker behavior.
Adding stochastic volatility or jump risk in the underlying would test whether the current well-posedness and numerical tractability survive richer dynamics.

Load-bearing premise

Option order flow is generated by Cox processes whose intensities depend on the underlying price and on the market maker's posted quotes, while hedging trades create both permanent and transient price impact on the underlying.

What would settle it

Market data or controlled simulations in which option order intensity shows no measurable response to underlying price or to posted quotes, or in which hedging trades produce neither permanent nor transient price shifts, would falsify the central dynamics.

Figures

Figures reproduced from arXiv: 2511.02518 by Etienne Chevalier, Paulin Aubert, Vathana Ly Vath.

**Figure 2.** Figure 2: Average quoting strategy (I0 = 0). As illustrated in Figure 3a, the agent’s strategy is to maintain its option inventory close to zero. This behavior is desirable for two reasons: first, it allows the agent to consistently capture spread revenues on the option market while generating sufficient order flow to avoid the activity penalty. Second, by keeping the inventory nearly balanced, the agent has no need… view at source ↗

**Figure 3.** Figure 3: Average inventories and P&L along trajectory. [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗

**Figure 4.** Figure 4: Sample path: underlying price and corresponding quoting behavior of the agent ( [PITH_FULL_IMAGE:figures/full_fig_p023_4.png] view at source ↗

**Figure 5.** Figure 5: Learning metrics for linear order book with [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗

**Figure 6.** Figure 6: Average mid-price and spread (I0 = −100). Turning to the quoting strategy, [PITH_FULL_IMAGE:figures/full_fig_p024_6.png] view at source ↗

**Figure 7.** Figure 7: Average quoting strategy (I0 = −100). The inventory dynamics reported in Figure 8a confirm this interpretation. The option inventory progressively converges toward zero as maturity approaches, while the underlying hedge position is gradually unwound. This two-step process ensures that both the hedging penalty and terminal risk are controlled. Finally, Figure 8b reports the cash trajectory. Unlike the symm… view at source ↗

**Figure 8.** Figure 8: Average inventories and P&L along trajectory. [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗

**Figure 9.** Figure 9: Shape of asymmetric option order flow intensities. [PITH_FULL_IMAGE:figures/full_fig_p025_9.png] view at source ↗

**Figure 10.** Figure 10: Average quoting strategy (I0 = 0 and asymmetric intensities). Figure 11a confirms this mechanism at the level of inventories. Starting from I0 = 0, the market maker’s option inventory drifts downward as client buy orders dominate, reaching significantly negative levels around the midpoint of the horizon. In the second half, the agent progressively buys back options in order to converge to a flat position … view at source ↗

**Figure 11.** Figure 11: Average inventories and P&L along trajectory. [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗

**Figure 12.** Figure 12: Average quoting strategy (I0 = −100 and low liquidity). As the horizon progresses, the agent gradually reduces its short option position, converging toward a nearly flat inventory at maturity (Figure 13a). This adjustment is accompanied by a progressive liquidation of the hedge position in the underlying, once the bulk of the initial coverage has been achieved. The cash dynamics are displayed in Figure 13… view at source ↗

**Figure 13.** Figure 13: Average inventories and P&L along trajectory. [PITH_FULL_IMAGE:figures/full_fig_p027_13.png] view at source ↗

read the original abstract

This paper develops a model for option market making in which the hedging activity of the market maker generates price impact on the underlying asset. The option order flow is modeled by Cox processes, with intensities depending on the state of the underlying and on the market maker's quoted prices. The resulting dynamics combine stochastic option demand with both permanent and transient impact on the underlying, leading to a coupled evolution of inventory and price. We first study market manipulation and arbitrage phenomena that may arise from the feedback between option trading and underlying impact. We then establish the well-posedness of the mixed control problem, which involves continuous quoting decisions and impulsive hedging actions. Finally, we implement a numerical method based on policy optimization to approximate optimal strategies and illustrate the interplay between option market liquidity, inventory risk, and underlying impact.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper couples option market making to hedging impact on the underlying via Cox processes and mixed controls, but the well-posedness claim under permanent-impact feedback needs the growth conditions checked.

read the letter

The core contribution is a market-making setup where the market maker's hedging trades move the underlying price through permanent and transient impact, and that price shift then changes the intensity of option order arrivals. This creates an explicit feedback loop between inventory, quoting, and the underlying dynamics that standard models usually keep separate. They also flag possible arbitrage or manipulation routes that the loop opens up before moving to the control problem itself. That combination of elements is the main novelty here, and it sits in a narrow but active corner of quantitative finance work on impact and liquidity provision. They establish well-posedness for the mixed control problem (continuous quoting plus impulsive hedging) and then run a policy-optimization scheme to approximate strategies and show how liquidity, inventory risk, and impact interact. The numerical examples are presented as illustrations rather than exhaustive tests, which is reasonable for this kind of paper. The potential weak point is exactly the one the stress test flags: whether the intensity functions stay integrable once permanent impact shifts the underlying price. If the dependence on the state variable is too strong, the compensator can explode and the value function becomes infinite. The abstract states that well-posedness holds, so the authors must have imposed linear-growth or boundedness conditions to close the loop, but those conditions are the part that needs explicit verification in the proofs. Without seeing the precise assumptions on the intensity map, it is hard to judge how restrictive they are or how well they match real option order flow. This work is aimed at researchers who already work with stochastic control and market-impact models in mathematical finance. A reader who cares about coupled inventory-price dynamics or about numerical methods for impulse-control problems will find concrete material to engage with. The technical level is high enough that it deserves a serious referee rather than a desk rejection; the feedback mechanism is worth checking even if the final conditions turn out to be somewhat strong. I would send it out for review and ask specifically for the growth restrictions used to guarantee finite value functions.

Referee Report

2 major / 2 minor

Summary. The paper develops a model for option market making in which the market maker's hedging trades generate both permanent and transient price impact on the underlying asset. Option order flow is represented by Cox processes whose intensities depend on the underlying price and the posted quotes. The resulting system is formulated as a mixed stochastic control problem combining continuous quoting decisions with impulsive hedging actions. The authors analyze potential market manipulation and arbitrage opportunities arising from the feedback loop, establish well-posedness of the control problem, and approximate optimal policies numerically via policy optimization to illustrate the trade-offs among option liquidity, inventory risk, and underlying impact.

Significance. If the well-posedness result holds under verifiable growth conditions and the numerical illustrations are reproducible, the work would provide a useful framework for studying self-induced impact in options market making, extending existing point-process and stochastic-control models in quantitative finance. The combination of permanent impact feedback with Cox-process demand is a natural but technically delicate extension that could inform practical risk-management considerations.

major comments (2)

[Abstract and dynamics formulation] The well-posedness claim for the mixed control problem (continuous quoting plus impulsive hedging) is central, yet the abstract and model description do not specify growth or boundedness conditions on the intensity function with respect to the underlying price S after permanent impact shifts. Without such restrictions, the compensator of the Cox process may explode in finite time, rendering the objective functional infinite and undermining the existence of an optimal value function.
[Well-posedness section] The feedback loop between permanent impact on S and the state-dependent intensity must be shown to preserve non-explosion of the controlled state processes. A concrete linear-growth or Lipschitz condition compatible with the permanent-impact drift term is required to close the well-posedness argument; its absence is load-bearing for the central mathematical claim.

minor comments (2)

[Model dynamics] Clarify the precise form of the transient impact kernel and its interaction with the impulsive hedging controls; a short remark on why the chosen kernel avoids additional singularities would improve readability.
[Numerical results] The numerical policy-optimization procedure would benefit from an explicit statement of the neural-network architecture, training horizon, and convergence diagnostics used to generate the reported strategies.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. The points raised about specifying growth conditions for well-posedness are important for clarity, and we will strengthen the manuscript accordingly. We respond to each major comment below.

read point-by-point responses

Referee: [Abstract and dynamics formulation] The well-posedness claim for the mixed control problem (continuous quoting plus impulsive hedging) is central, yet the abstract and model description do not specify growth or boundedness conditions on the intensity function with respect to the underlying price S after permanent impact shifts. Without such restrictions, the compensator of the Cox process may explode in finite time, rendering the objective functional infinite and undermining the existence of an optimal value function.

Authors: We agree that explicit growth conditions should be stated upfront. The well-posedness analysis relies on the intensity satisfying a linear growth bound in S (of the form λ ≤ C(1 + |S|)) to control the compensator after permanent impact updates. To address the concern directly, we will revise the model formulation section to introduce this as a standing assumption and update the abstract to note that well-posedness holds under these verifiable conditions. This will make the non-explosion of the Cox process explicit. revision: yes
Referee: [Well-posedness section] The feedback loop between permanent impact on S and the state-dependent intensity must be shown to preserve non-explosion of the controlled state processes. A concrete linear-growth or Lipschitz condition compatible with the permanent-impact drift term is required to close the well-posedness argument; its absence is load-bearing for the central mathematical claim.

Authors: The referee correctly notes that the feedback requires explicit control. The permanent impact enters as a linear drift in the S-dynamics, and the intensity is taken to be Lipschitz in S. We will expand the well-posedness section with a dedicated lemma that applies a Gronwall-type estimate to the integrated intensity, showing that the linear growth and Lipschitz assumptions close the argument and rule out finite-time explosion for admissible controls. The revised proof will be self-contained. revision: yes

Circularity Check

0 steps flagged

No significant circularity; well-posedness follows from stated stochastic assumptions

full rationale

The paper models option flows via Cox processes with state-dependent intensities, incorporates permanent/transient impact on the underlying, and then establishes well-posedness of the resulting mixed control problem before turning to numerical policy optimization. These steps rely on standard existence results for controlled point processes and impulse control under linear-growth or bounded-intensity conditions; no equation or claim reduces by construction to a fitted parameter, self-defined quantity, or self-citation chain. The central claims remain independent of the numerical illustrations.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard domain assumptions from stochastic processes and market-impact modeling; no new entities are postulated, but functional forms for intensities and impact kernels are required and treated as modeling choices.

free parameters (1)

intensity dependence parameters
The Cox process intensities are stated to depend on underlying state and quoted prices, requiring specific functional forms or parameter values to close the model.

axioms (2)

domain assumption Option order flow follows Cox processes with state- and price-dependent intensities
Explicitly used to model stochastic demand in the abstract.
domain assumption Hedging generates both permanent and transient price impact on the underlying
Invoked to produce the coupled inventory-price dynamics.

pith-pipeline@v0.9.0 · 5659 in / 1598 out tokens · 50880 ms · 2026-05-18T01:35:01.897911+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The option order flow is modeled by Cox processes, with intensities depending on the state of the underlying and on the market maker's quoted prices... both permanent and transient impact on the underlying... mixed control problem... continuous quoting decisions and impulsive hedging actions.
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Theorem 3.1 (Well-posedness and quadratic bounds)... value function v ... finite ... quadratic growth estimates

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages

[1]

Optimal execution and price manipulations in time- varying limit order books

Aurélien Alfonsi and José Infante Acevedo. “Optimal execution and price manipulations in time- varying limit order books”. In:Applied Mathematical Finance21.3 (2014), pp. 201–237.doi:10. 1080/1350486X.2013.845471

work page arXiv 2014
[2]

Dynamic optimal execution in a mixed-market-impact Hawkes price model

Aurélien Alfonsi and Pierre Blanc. “Dynamic optimal execution in a mixed-market-impact Hawkes price model”. In:Finance and Stochastics20.1 (2016), pp. 183–218.issn: 1432-1122.doi:10.1007/ s00780-015-0282-y

work page 2016
[3]

Optimal execution of portfolio transactions

Robert Almgren and Neil Chriss. “Optimal execution of portfolio transactions”. In:Journal of Risk 3 (2001), pp. 5–40.doi:10.21314/JOR.2001.041. 27

work page doi:10.21314/jor.2001.041 2001
[4]

High Frequency Trading in a Limit Order Book

Marco Avellaneda and Sasha Stoikov. “High-frequency trading in a limit order book”. In:Quanti- tative Finance8.3 (2008), pp. 217–224.doi:10.1080/14697680701381228

work page doi:10.1080/14697680701381228 2008
[5]

Algorithmic market making for options

Bastien Baldacci, Philippe Bergault, and Olivier Guéant. “Algorithmic market making for options”. In:Quantitative Finance21.1 (2021), pp. 85–97.doi:10.1080/14697688.2020.1766099

work page doi:10.1080/14697688.2020.1766099 2021
[6]

Buehler, L

Hans Buehler et al. “Deep hedging”. In:Quantitative Finance19.8 (2019), pp. 1271–1291.doi: 10.1080/14697688.2019.1571683

work page doi:10.1080/14697688.2019.1571683 2019
[7]

Optimal execution with limit and market orders

Álvaro Cartea and Sebastian Jaimungal. “Optimal execution with limit and market orders”. In: Quantitative Finance15 (May 2015), pp. 1–13.doi:10.1080/14697688.2015.1032543

work page doi:10.1080/14697688.2015.1032543 2015
[8]

Buy Low, Sell High: A High Frequency Trading Perspective

Álvaro Cartea, Sebastian Jaimungal, and Jason Ricci. “Buy Low, Sell High: A High Frequency Trading Perspective”. In:SIAM Journal on Financial Mathematics5.1 (2014), pp. 415–444.doi: 10.1137/130911196

work page doi:10.1137/130911196 2014
[9]

A Stochastic Control Approach to Option Market Making

Sofiene El Aoud and Frédéric Abergel. “A Stochastic Control Approach to Option Market Making”. In:SSRN Electronic Journal01 (July 2015).doi:10.2139/ssrn.2491446

work page doi:10.2139/ssrn.2491446 2015
[10]

DynamicalModelsofMarketImpactandAlgorithmsforOrder Execution

JimGatheralandAlexanderSchied.“DynamicalModelsofMarketImpactandAlgorithmsforOrder Execution”. In:SSRN Electronic Journal(Jan. 2013), pp. 579–599.doi:10.2139/ssrn.2034178

work page doi:10.2139/ssrn.2034178 2013
[11]

Dealing with the Inventory Risk. A solution to the market making problem

Olivier Guéant, Charles-Albert Lehalle, and Joaquin Fernandez Tapia. “Dealing with the Inventory Risk. A solution to the market making problem”. In:Mathematics and Financial Economics7.4 (2013), pp. 477–507.doi:10.1007/s11579-012-0087-0

work page doi:10.1007/s11579-012-0087-0 2013
[12]

Optimal High Frequency Trading with Limit and Market Orders

Fabien Guilbaud and Huyên Pham. “Optimal High Frequency Trading with Limit and Market Orders”. In:Quantitative Finance13 (June 2011).doi:10.1080/14697688.2012.708779

work page doi:10.1080/14697688.2012.708779 2011
[13]

Price manipulation and quasi-arbitrage

Gur Huberman and Werner Stanzl. “Price manipulation and quasi-arbitrage”. In:Econometrica 72.4 (2004), pp. 1247–1275.doi:10.1111/j.1468-0262.2004.00531.x

work page doi:10.1111/j.1468-0262.2004.00531.x 2004
[14]

Optimal Execution in a General One-Sided Limit-Order Book

Silviu Predoiu, Gennady Shaikhet, and Steven Shreve. “Optimal Execution in a General One-Sided Limit-Order Book”. In:SIAM J. Financial Math.2 (Jan. 2011), pp. 183–212.doi:10 . 1137 / 10078534X

work page 2011
[15]

Market Making via Reinforcement Learning

Thomas Spooner et al. “Market Making via Reinforcement Learning”. In:Proceedings of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2018). 2018. url:https://dl.acm.org/doi/10.5555/3237383.3237450

work page doi:10.5555/3237383.3237450 2018
[16]

Option market making under inventory risk

Sasha Stoikov and Mehmet Sağlam. “Option market making under inventory risk”. In:Review of Derivatives Research12.1 (Apr. 2009), pp. 55–79.doi:10.1007/s11147-009-9036-3. A Technical proofs A.1 Stability and moment estimates We establish stability and moment bounds for the Hawkes intensities and the state variables, which are then propagated to the price, ...

work page doi:10.1007/s11147-009-9036-3 2009

[1] [1]

Optimal execution and price manipulations in time- varying limit order books

Aurélien Alfonsi and José Infante Acevedo. “Optimal execution and price manipulations in time- varying limit order books”. In:Applied Mathematical Finance21.3 (2014), pp. 201–237.doi:10. 1080/1350486X.2013.845471

work page arXiv 2014

[2] [2]

Dynamic optimal execution in a mixed-market-impact Hawkes price model

Aurélien Alfonsi and Pierre Blanc. “Dynamic optimal execution in a mixed-market-impact Hawkes price model”. In:Finance and Stochastics20.1 (2016), pp. 183–218.issn: 1432-1122.doi:10.1007/ s00780-015-0282-y

work page 2016

[3] [3]

Optimal execution of portfolio transactions

Robert Almgren and Neil Chriss. “Optimal execution of portfolio transactions”. In:Journal of Risk 3 (2001), pp. 5–40.doi:10.21314/JOR.2001.041. 27

work page doi:10.21314/jor.2001.041 2001

[4] [4]

High Frequency Trading in a Limit Order Book

Marco Avellaneda and Sasha Stoikov. “High-frequency trading in a limit order book”. In:Quanti- tative Finance8.3 (2008), pp. 217–224.doi:10.1080/14697680701381228

work page doi:10.1080/14697680701381228 2008

[5] [5]

Algorithmic market making for options

Bastien Baldacci, Philippe Bergault, and Olivier Guéant. “Algorithmic market making for options”. In:Quantitative Finance21.1 (2021), pp. 85–97.doi:10.1080/14697688.2020.1766099

work page doi:10.1080/14697688.2020.1766099 2021

[6] [6]

Buehler, L

Hans Buehler et al. “Deep hedging”. In:Quantitative Finance19.8 (2019), pp. 1271–1291.doi: 10.1080/14697688.2019.1571683

work page doi:10.1080/14697688.2019.1571683 2019

[7] [7]

Optimal execution with limit and market orders

Álvaro Cartea and Sebastian Jaimungal. “Optimal execution with limit and market orders”. In: Quantitative Finance15 (May 2015), pp. 1–13.doi:10.1080/14697688.2015.1032543

work page doi:10.1080/14697688.2015.1032543 2015

[8] [8]

Buy Low, Sell High: A High Frequency Trading Perspective

Álvaro Cartea, Sebastian Jaimungal, and Jason Ricci. “Buy Low, Sell High: A High Frequency Trading Perspective”. In:SIAM Journal on Financial Mathematics5.1 (2014), pp. 415–444.doi: 10.1137/130911196

work page doi:10.1137/130911196 2014

[9] [9]

A Stochastic Control Approach to Option Market Making

Sofiene El Aoud and Frédéric Abergel. “A Stochastic Control Approach to Option Market Making”. In:SSRN Electronic Journal01 (July 2015).doi:10.2139/ssrn.2491446

work page doi:10.2139/ssrn.2491446 2015

[10] [10]

DynamicalModelsofMarketImpactandAlgorithmsforOrder Execution

JimGatheralandAlexanderSchied.“DynamicalModelsofMarketImpactandAlgorithmsforOrder Execution”. In:SSRN Electronic Journal(Jan. 2013), pp. 579–599.doi:10.2139/ssrn.2034178

work page doi:10.2139/ssrn.2034178 2013

[11] [11]

Dealing with the Inventory Risk. A solution to the market making problem

Olivier Guéant, Charles-Albert Lehalle, and Joaquin Fernandez Tapia. “Dealing with the Inventory Risk. A solution to the market making problem”. In:Mathematics and Financial Economics7.4 (2013), pp. 477–507.doi:10.1007/s11579-012-0087-0

work page doi:10.1007/s11579-012-0087-0 2013

[12] [12]

Optimal High Frequency Trading with Limit and Market Orders

Fabien Guilbaud and Huyên Pham. “Optimal High Frequency Trading with Limit and Market Orders”. In:Quantitative Finance13 (June 2011).doi:10.1080/14697688.2012.708779

work page doi:10.1080/14697688.2012.708779 2011

[13] [13]

Price manipulation and quasi-arbitrage

Gur Huberman and Werner Stanzl. “Price manipulation and quasi-arbitrage”. In:Econometrica 72.4 (2004), pp. 1247–1275.doi:10.1111/j.1468-0262.2004.00531.x

work page doi:10.1111/j.1468-0262.2004.00531.x 2004

[14] [14]

Optimal Execution in a General One-Sided Limit-Order Book

Silviu Predoiu, Gennady Shaikhet, and Steven Shreve. “Optimal Execution in a General One-Sided Limit-Order Book”. In:SIAM J. Financial Math.2 (Jan. 2011), pp. 183–212.doi:10 . 1137 / 10078534X

work page 2011

[15] [15]

Market Making via Reinforcement Learning

Thomas Spooner et al. “Market Making via Reinforcement Learning”. In:Proceedings of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2018). 2018. url:https://dl.acm.org/doi/10.5555/3237383.3237450

work page doi:10.5555/3237383.3237450 2018

[16] [16]

Option market making under inventory risk

Sasha Stoikov and Mehmet Sağlam. “Option market making under inventory risk”. In:Review of Derivatives Research12.1 (Apr. 2009), pp. 55–79.doi:10.1007/s11147-009-9036-3. A Technical proofs A.1 Stability and moment estimates We establish stability and moment bounds for the Hawkes intensities and the state variables, which are then propagated to the price, ...

work page doi:10.1007/s11147-009-9036-3 2009