On the uniqueness of classical solutions of Cauchy problems

Erhan Bayraktar and 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.

Date: 2009-08, Revised 2009-09
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:0908.1086

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