In the classic mean-variance portfolio theory as proposed by Harry Markowitz, the weights of the optimized portfolios are directly proportional to the inverse of the asset correlation matrix. However, most of contemporary portfolio optimization research focuses on optimizing the correlation...

Several exchanges in futures and options deploy pro-rata matching. The executed size of limit orders in pro-rata markets is never certain, unlike in price-time priority matching systems. This article derives the optimal size of limit orders in pro-rata markets given the trader's desired...

The current research assesses the risks commonly attributed to the presence of HFT in the context of different market structures deployed by the U.S. exchanges. In particular, we find that, by design, the so-called “normal” exchanges have the lowest market quality, including the highest...