Stability of the exponential utility maximization problem with respect to preferences

This paper studies stability of the exponential utility maximization when there are small variations on agent's utility function. Two settings are considered. First, in a general semi-martingale model where random endowments are present, a sequence of utilities depned on R converges to the exponential utility. Under a uniform condition on their marginal utilities, convergence of value functions, optimal payouts and optimal investment strategies are obtained, their rate of con-vergence are also determined. Stability of utility-based pricing is studied as an application. Second, a sequence of utilities depened on R+ converges to the exponential utility after shifting and scaling. Their associated optimal strategies, after appropriate scaling, converge to the optimal strategy for the exponential hedging problem. This complements Theorem 3.2 in M. Nutz, Probab. Theory Relat. Fields, 152, 2012, which establishes the convergence for a sequence of power utilities.