Exponential investors with weakly mean-reverting prices

Abstract

We investigate a continuous-time financial market where the asset price exhibits weak (sublinear) mean reversion and has a nonzero drift. Complementing earlier work on strong (superlinear) mean reversion, we show that, for an investor maximizing expected exponential utility, the certainty equivalent grows as $O(T^{2\beta+1})$ where $0<\beta<1$ is the strength of mean reversion. An explicit asymptotically optimal strategy is also given.