In this study, the author proposes an optimization framework for market-making in a limit-order book, based on the theory of stochastic approximation. The idea is to take advantage of the iterative nature of the process of updating bid and ask quotes in order to make the algorithm optimize its strategy on a trial-and-error basis (i.e. on-line learning). An advantage of this approach is that the exploration of the system by the algorithm is performed in run-time, so explicit specifications of the price dynamics are not necessary, as is the case in the stochastic-control approach.
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