We propose a model of dynamic trading where a strategic high frequency trader receives an imperfect signal about future order flows, and exploits his speed advantage to optimize his quoting policy. We determine the provision of liquidity, order cancellations, and impact on low frequency traders...

We solve a portfolio choice problem when expected returns, volatilities and trading-costs follow a regime-switching model. The optimal policy trades towards an aim portfolio given by a weighted-average of the conditional mean-variance portfolios in all future states. The trading speed is higher...