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On the uniqueness of classical solutions of Cauchy problems

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Given that the terminal condition is of at most linear growth, it is well known that a Cauchy problem admits a unique classical solution when the coefficient multiplying the second derivative is also a function of at most linear growth. In this paper, we give a condition on the volatility that is necessary and sufficient for a Cauchy problem to admit a unique solution.

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en

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http://eprints.lse.ac.uk/31871/

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