In this talk, we will look at the mathematics of a couple of price impact models and analyze several optimization problems that arise in the context of algorithmic trading. These optimization problems will be formulated as singular control problems but solved by means of (stochastic) integral representations. This allows us in particular to work in a non‐Markovian setting. Our analysis will exhibit some interesting mathematical properties of the optimal strategies. Some of these results might contribute to the evaluation of the underlying models. For instance, we will find that transience of price impact can lead to somewhat unstable optimal strategies. Some other results are of interest from a purely mathematical point of view. For example, we are led to minimizing Cartan energy forms by means of optimal control techniques.
The talk includes joint work with Aurélien Alfonsi and with Christopher Lorenz.