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On the martingale property of stochastic exponentials. (English) Zbl 1066.60064

The authors present a necessary and sufficient condition for stochastic exponential to be a true martingale. The condition is formulated in terms of nonexplosion of some “functional” process connected with exponential. An alternative interpretation of this result is that the stochastic exponential is a true martinagale if and only if under a “candidate measure” the integrand process is square integrable over time. Some examples and counterexamples are considered including the applications to mathematical finance.

MSC:

60H30 Applications of stochastic analysis (to PDEs, etc.)
91B28 Finance etc. (MSC2000)
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References:

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