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arXiv · 2512.20850

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

Alexey Meteykin
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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. 2025-12-24. Implicit Numerical Scheme for the Hamilton-Jacobi-Bellman Quasi-Variational Inequality in the Optimal Market-Making Problem with Alpha Signal. https://arxiv.org/abs/2512.20850

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