In this paper we show that the optimal exercise boundary/free boundary of the American put option pricing problem for jump diffusions is continuously differentiable (except at maturity). This differentiability result was established by Yang, Jiang, and Bian [European J. Appl. Math., 17 (2006), pp. 95–127] in the case where the condition $r\geq q+\lambda\int_{\mathbb{R}_+}\,(e^z-1)\,\nu(dz)$ is satisfied. We extend the result to the case where the condition fails using a unified approach that treats both cases simultaneously. We also show that the boundary is infinitely differentiable under a regularity assumption on the jump distribution.
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机译：在本文中，我们表明跳扩散的美国看跌期权定价问题的最优行使边界/自由边界是可连续微分的（到期除外）。这种可区分性结果是由Yang，Jiang和Bian [European J. Appl。 Math。（17）（2006），第95–127页]，其中条件$ r \ geq q + \ lambda \ int _ {\ mathbb {R} _ +} \，（e ^ z-1）\，\ nu（dz）$是满意的。我们使用统一的方法同时处理这两种情况，将结果扩展到条件失败的情况。我们还表明，在跳跃分布的规则性假设下，边界是无限可微的。
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