On the uniqueness of classical solutions of Cauchy problems

@article{Bayraktar2009OnTU,
title={On the uniqueness of classical solutions of Cauchy problems},
author={Erhan Bayraktar and Hao Xing},
journal={arXiv: Analysis of PDEs},
year={2009}
}
• Published 7 August 2009
• Mathematics
• arXiv: Analysis of PDEs
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 (i.e., the volatility) is also a function of at most linear growth. In this note, 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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