On the Existence of Martingale Measures in Jump Diffusion Market Models
Abstract
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 con- sider an example with constraints on the portfolio that go beyond the standard ones for admissibility.
Keywords
Cite
@article{arxiv.1511.08349,
title = {On the Existence of Martingale Measures in Jump Diffusion Market Models},
author = {Jacopo Mancin and Wolfgang J. Runggaldier},
journal= {arXiv preprint arXiv:1511.08349},
year = {2015}
}
Comments
A version has appeared in "Arbitrage, Credit and Informational Risks", Peking University Series in Mathematics Vol.5, World Scientific 2014. Arbitrage, Credit and Informational Risks, (C. Hillairet, M. Jeanblanc, Y. Jiao, eds.). Peking University Series in Mathematics, Vol.5, World Scientific Publishing Co. Pte. Ltd., 2014, pp.29-51