Optimal incentives in a limit order book: a SPDE control approach

With the fragmentation of electronic markets, exchanges are now competing in order to attract trading activity on their platform. Consequently, they developed several regulatory tools control liquidity provision / consumption pool. In this paper, we study problem an exchange using incentives increase market liquidity. We model limit book as solution a stochastic partial differential equation (SPDE) [12]. The proposed participants functions time and distance mid-price. formulate who wishes modify shape by increasing volume at specific limits. Due particular nature SPDE problem, able characterize with classic Feynman-Kac representation theorem. Moreover, when studying asymptotic behavior solution, penalty function enables obtain closed-form each book. numerically form impact book, analyze sensitivity parameters.