On the uniqueness of classical solutions of Cauchy problems

Details On the uniqueness of classical solutions of Cauchy problems On the uniqueness of classical solutions of Cauchy problems

2009-08-07

arxiv.org/abs/0908.1086v7

Mathematics

Analysis of PDEs

Key Words and Phrases: Cauchy problem, a necessary and sufficient condition for uniqueness, European call-type options, Strict

Scientific paper

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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