Under which condition does the optimal insurance demand decrease in wealth? In the expected utility model a decreasing concavity condition is necessary and sufficient for this result. However in general, the result does not hold under ambiguity aversion. By introducing several types of controlling relation about random loss variables, we constrained the structure of the ambiguity and obtained several unambiguous results. The results show that under these constraints the demand for insurance against ambiguous losses also decreases in wealth.