Abstract
Using the Ray-Knight theorem we give conditions for anonnegative diffusion without drift to reach zero or not. These results also givenecessary and sufficient conditions for such a diffusion process to be a martingale (and notjust a local martinagle). We apply these results in order to give necessary and sufficientconditions for nonnegative diffusion to have equivalent local martingale measures.
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References
Revuz, D. and Yor, M. (1991) Continuous Martingales and Brownian Motion, Springer-Verlag.
Ikeda, N. and Watanabe, S. (1981) Stochastic Differential Equations and Diffusion Processes, North-Holland Publ Co., Amsterdam; Kodansha Ltd, Tokyo.
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Delbaen, F., Shirakawa, H. No Arbitrage Condition for Positive Diffusion Price Processes. Asia-Pacific Financial Markets 9, 159–168 (2002). https://doi.org/10.1023/A:1024173029378
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DOI: https://doi.org/10.1023/A:1024173029378