Stability of exponential utility maximization with respect to market perturbations

We investigate the continuity of expected exponential utility maximization with respect to perturbation of the Sharpe ratio of markets. By focusing only on continuity, we impose weaker regularity conditions than those found in the literature. Specifically, we require, in addition to the VV-compactness hypothesis of Larsen and Žitković (2007) [13], a local bmobmo hypothesis, a condition which is essentially implicit in the setting of [13]. For markets of the form S=M+∫λd〈M〉S=M+∫λd〈M〉, these conditions are simultaneously implied by the existence of a uniform bound on the norm of λ⋅Mλ⋅M in a suitable bmobmo space.