Abstract
This paper studies a comparison theorem for solutions of stochastic differential equations and its generalization to the multi-dimensional case. We show, that even though the proof of the generalized theorem follows that of the one-dimensional comparison theorem, the multi-dimensional case requires a different condition on the drift coefficient, known in the theory of differential equations as Kamke-Wazewski condition. We also present several examples of possible applications to option price estimation in finance.
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