Stability of the Utilitymaximization Problemwith Random Endowment in Incomplete Markets

We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (asmodeled via expected utility), as well as views of the world or the market model (as modeled via subjective probabilities) are considered. Simple sufficient conditions are given for the problem to be well posed, in the sense that the optimal wealth and the marginal utility-based prices are continuous functionals of preferences and probabilistic views.