We consider the problem of pricing perpetual American options written on dividend-paying assets whose price dynamics follow a multidimensional Black and Scholes model. For convex Lipschitz continuous reward functions, we give a probabilistic characterization of the fair price in terms of a reflected BSDE, and an analytical one in terms of an obstacle problem. We also provide the early exercise premium formula.

中文翻译：

---

多维布莱克-斯科尔斯模型中的永续美式期权

我们考虑以派息资产为基础的永续美式期权定价问题，其价格动态遵循多维布莱克和斯科尔斯模型。对于凸 Lipschitz 连续奖励函数，我们根据反射 BSDE 给出公平价格的概率表征，并根据障碍问题给出分析表征。我们还提供早期锻炼保费公式。