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Implicit Numerical Scheme for the Hamilton-Jacobi-Bellman Quasi-Variational Inequality in the Optimal Market-Making Problem with Alpha Signal

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  • Alexey Meteykin

Abstract

We address the problem of combined stochastic and impulse control for a market maker operating in a limit order book. The problem is formulated as a Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI). We propose an implicit time-discretization scheme coupled with a policy iteration algorithm. This approach removes time-step restrictions typical of explicit methods and ensures unconditional stability. Convergence to the unique viscosity solution is established by verifying monotonicity, stability, and consistency conditions and applying the comparison principle.

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  • Alexey Meteykin, 2025. "Implicit Numerical Scheme for the Hamilton-Jacobi-Bellman Quasi-Variational Inequality in the Optimal Market-Making Problem with Alpha Signal," Papers 2512.20850, arXiv.org.
    • Handle: RePEc:arx:papers:2512.20850
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    References listed on IDEAS

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    1. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
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