\noindent We address the issue of market making on electronic markets when taking into account the self exciting property of market order flow . We consider a market with order flows driven by Hawkes processes where one market makeroperates, aiming at optimizing its profit . We characterize an optimal control solving this problem by proving existence and uniqueness of a viscosity solution to the associated Hamilton Jacobi Bellman equation. Finally we propose a methodology to approximate the optimal strategy .
\noindent We address the issue of market making on electronic markets when taking into account the clustering and long memory properties of market order flows . We consider a market model with one market maker and order flows driven by general Hawkes processes. We formulate the market maker's objective as a stochastic control problem . We characterize an optimal control by proving existence and uniqueness of a viscosity solution to the associated Hamilton-Jacobi-Bellman equation. Finally we propose a fully consistent numerical method allowing to implement this optimal strategy in practice .
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self exciting property
clustering and long memory properties
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flow
flows
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with
model with one market maker and
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Hawkes processes where one market makeroperates, aiming at optimizing its profit
general Hawkes processes. We formulate the market maker's objective as a stochastic control problem
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solving this problem
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Hamilton Jacobi Bellman
Hamilton-Jacobi-Bellman
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methodology to approximate the optimal strategy
fully consistent numerical method allowing to implement this optimal strategy in practice