In the context of jump-diffusion market models we construct examples that satisfy the weaker no-arbitrage condition of NA1 (NUPBR), but not NFLVR. We show that in these examples the only candidate for the density process of an equivalent local martingale measure is a supermartingale that is not a martingale, not even a local martingale. This candidate is given by the supermartingale deflator resulting from the inverse of the discounted growth optimal portfolio. In particular, we consider an example with constraints on the portfolio that go beyond the standard ones for admissibility.

which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.Abstract We study the concept of financial bubbles in a market model endowed with a set P of probability measures, typically mutually singular to each other. In this setting, we investigate a dynamic version of robust superreplication, which we use to introduce the notions of bubble and robust fundamental value in a way consistent with the existing literature in the classical case P = {P}. Finally, we provide concrete examples illustrating our results.

In this paper we study mean-variance hedging under the G-expectation framework. Our analysis is carried out by exploiting the G-martingale representation theorem and the related probabilistic tools, in a continuous financial market with two assets, where the discounted risky one is modeled as a symmetric G-martingale. By tackling progressively larger classes of contingent claims, we are able to explicitly compute the optimal strategy under general assumptions on the form of the contingent claim.

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