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On the uniqueness of classical solutions of Cauchy problems
Author(s):
Erhan
Bayraktar;
Hao
Xing
Journal:
Proc. Amer. Math. Soc.
138
(2010),
2061-2064.
MSC (2010):
Primary 35K65, 60G44
Posted:
January 27, 2010
MathSciNet review:
2596042
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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 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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Additional Information:
Erhan
Bayraktar
Affiliation:
Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, Michigan 48104
Email:
erhan@umich.edu
Hao
Xing
Affiliation:
Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215
Email:
haoxing@bu.edu
DOI:
10.1090/S0002-9939-10-10306-2
PII:
S 0002-9939(10)10306-2
Keywords:
Cauchy problem,
a necessary and sufficient condition for uniqueness,
European call-type options,
strict local martingales
Received by editor(s):
September 16, 2009
Posted:
January 27, 2010
Additional Notes:
This research is supported in part by the National Science Foundation under grant number DMS-0906257.
Communicated by:
Edward C. Waymire
Copyright of article:
Copyright
2010,
By the authors
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