On exponential local martingales associated with strong Markov continuous local martingales
We investigate integral functionals , t>=0, where m is a nonnegative measure on and LY is the local time of a Wiener process with drift, i.e.,Â Yt=Wt+t, t>=0, with a standard Wiener process W. We give conditions for a.s. convergence and divergence of Tt, t>=0, and T[infinity]. In the second part of the present note we apply these results to exponential local martingales associated with strong Markov continuous local martingales. In terms of the speed measure of a strong Markov continuous local martingale, we state a necessary and sufficient condition for the exponential local martingale associated with a strong Markov continuous local martingale to be a martingale.
Volume (Year): 119 (2009)
Issue (Month): 9 (September)
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- David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48.
- Tina Hviid Rydberg, 1997. "A note on the existence of unique equivalent martingale measures in a Markovian setting," Finance and Stochastics, Springer, vol. 1(3), pages 251-257.
- Albert N. Shiryaev & Jan Kallsen, 2002. "The cumulant process and Esscher's change of measure," Finance and Stochastics, Springer, vol. 6(4), pages 397-428.
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