Before revision: We consider a semi-static market composed of derivative securities, which we assume can be traded only at time zero, and of stocks, which can be traded continuously in time  . Using a general utility function defined on the positive real line, we study the dependence on the price of the derivatives of the outputs of the utility maximization problem  , investigating not only stability but also differentiability, monotonicity, convexity and asymptotic properties.
After revision: We consider a semi-static market composed of derivative securities, which we assume can be traded only at time zero, and of stocks, which can be traded continuously in time and are modeled as locally-bounded semi-martingales . Using a general utility function defined on the positive real line, we study the dependence on the price of the derivatives of the outputs of the utility maximization problem , investigating not only stability but also differentiability, monotonicity, convexity and asymptotic properties.