| Abstract: |
| We study an optimal market-making problem under which the order flow and liquidity level are driven by self-exciting Hawkes processes. To overcome the challenge brought by the non-Markovian structure of the problem, we propose a Markovian lifting approach where the Hawkes kernels are approximated by their truncated Mercer`s expansions. This enables dynamic programming and in turn computationally feasible procedures to solve the market-making problem. The theoretical convergence of the approximated solution to the true value function is proven. Our numerical findings show that ignoring persistence with the the order flow and liquidity level underestimates adverse selection risk, whereas explicitly modelling them improves the robustness and profitability of the market-making strategies. |
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