A free boundary problem arising from pricing convertible bond

In this article we study the behaviours of the optimal conversion boundary (i.e. free boundary) of an American-style convertible bond with finite horizon (i.e. parabolic case). We prove the existence and the uniqueness of the strong solution of the problem and the boundedness and smoothness of the free boundary. Moreover, we characterize the free boundary's start point and present two numerical results.

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