In this paper we outline initial concepts for an immune inspired algorithm to evaluate price time series data. The proposed solution evolves a short term pool of trackers dynamically through a process of proliferation and mutation, with each member attempting to map to trends in price movements....

We consider a Nash equilibrium between two high-frequency traders in a simple market impact model with transient price impact and additional quadratic transaction costs. Extending a result by Sch\"oneborn (2008), we prove existence and uniqueness of the Nash equilibrium and show that for small...

We consider $n$ risk-averse agents who compete for liquidity in an Almgren--Chriss market impact model. Mathematically, this situation can be described by a Nash equilibrium for a certain linear-quadratic differential game with state constraints. The state constraints enter the problem as...