The paper contains necessary and sufficient conditions for a closed convex set of measures to satisfy the property of multiplicative stability. One of the examples of multiplicatively stable convex sets is the set of absolutely continuous risk neutral measures for an arbitrage free price process. The conditions mentioned above are related to concepts such as price of risk and fit well in economic theory. Applying this characterization to the situation of arbitrage free risk processes, the author gives a characterization of those sets that can arise as sets of risk neutral measures. In the case of filtration where all martingales are continuous, the problem is solved completely.
For the entire collection see [Zbl 1092.60003].