Optimal Execution with Quadratic Variation Inventories

The first half of the paper is devoted to description and implementation statistical tests arguing for presence a Brownian component in inventories wealth processes individual traders. We use intra-day data from Toronto Stock Exchange provide empirical evidence this claim. work with regularly spaced time intervals, as well asynchronously observed data. reveal high significance non-zero motion component. second concerned analysis trader behaviors throughout day. extend theoretical an existing optimal execution model accommodate It\^o inventory processes, we compare empirically behavior traders such fitted models, their actual inferred