Pairs trading of two assets with uncertainty in co-integration's level of mean reversion

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 for utility function U(x) = x1-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 < γ < 1 there remains potential for infinite value functions in finite time. Also, we quantify the expected loss in utility due to partial information, and present a numerical study to illustrate the contribution of this paper.