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arXiv · 0908.1086

On the uniqueness of classical solutions of Cauchy problems

Erhan Bayraktar·Hao Xing
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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 (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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Erhan Bayraktar, Hao Xing. 2009-09-16. On the uniqueness of classical solutions of Cauchy problems. https://arxiv.org/abs/0908.1086

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