Pairs Trading of Two Assets with Uncertainty in Co-Integration's Level of Mean Reversion

Abstract

This paper considers a stochastic control problem derived from a model for pairs trading under incomplete information. We decompose an individual asset’s drift into two parts: an industry drift plus some additional stochasticity. The extra stochasticity may be unobserved, which means the investor has only partial information. We solve the control problem under both full and partial information for utility function U(x) = x^{1−γ}/(1−γ), and we make comparisons. We show the existence of stable solution to the associated matrix Riccati equations in both cases for γ > 1, but for 0