On the uniqueness of classical solutions of Cauchy problems

Bayraktar, Erhan; Xing, Hao

doi:10.1090/S0002-9939-10-10306-2

On the uniqueness of classical solutions of Cauchy problems
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by Erhan Bayraktar and Hao Xing PDF

Proc. Amer. Math. Soc. 138 (2010), 2061-2064

Abstract:

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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