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 . 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 limiting properties.