On the Martingale Property of Certain Local Martingales: Criteria and Applications

@inproceedings{Mijatovic2009OnTM,
  title={On the Martingale Property of Certain Local Martingales: Criteria and Applications},
  author={Aleksandar Mijatovic and Mikhail Urusov},
  year={2009}
}
The stochastic exponential Zt = exp{Mt − M0 − (1/2)〈M,M〉t} of a continuous local martingale M is itself a continuous local martingale. We give a necessary and sufficient condition for the process Z to be a true martingale in the case where Mt = ∫ t 0 b(Yu) dWu and Y is a one-dimensional diffusion driven by a Brownian motion W . Furthermore, we provide a necessary and sufficient condition for Z to be a uniformly integrable martingale in the same setting. These conditions are deterministic and… CONTINUE READING
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