Finding Moving-Band Statistical Arbitrages via Convex-Concave
  Optimization
Kasper Johansson Thomas Schmelzer Stephen Boyd
We propose a new method for finding statistical arbitrages that can contain
more assets than just the traditional pair. We formulate the problem as seeking
a portfolio with the highest volatility, subject to its price remaining in a
band and a leverage limit. This optimization problem is not convex, but can be
approximately solved using the convex-concave procedure, a specific sequential
convex programming method. We show how the method generalizes to finding
moving-band statistical arbitrages, where the price band midpoint varies over
time.