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 (S...

In this paper, we derive new, nearly optimal bounds for the Gaussian approximation to scaled averages of n independent high-dimensional centered random vectors X1,…,Xn over class rectangles in case when covariance matrix average is nondegenerate. bounded Xi’s, implied bound Kolmogorov distance between distribution and vector takes form C(Bn2log3d/n)1/2logn, where d dimension Bn a uniform envelo...

We study a McKean–Vlasov optimal control problem with common noise in order to establish the corresponding limit theory as well equivalence between different formulations, including strong, weak, and relaxed formulations. In contrast strong formulation, which is formulated on fixed probability space equipped two Brownian filtrations, weak formulation obtained by considering more general filtrat...