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 informations and show the existence of stable solution to the associated matrix Riccati equations. We quantify the expected loss in utility due to partial information, and present a numerical study to illustrate the contribution of this paper.