Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in which some of the properties |volatility and dividend policy| of the underlying stock can change at a random instant of time, but in such a way that we can forecast their final values. Under this assumption we can model actual market conditions because most relevant facts usually entail sharp predictable consequences. The effect of this potential risk on perpetual American vanilla options is remarkable: the very equation that will determine the fair price depends on the solution to be found. Sound results are found under the optics both of finance and physics. In particular, a parallelism among the overall outcome of this problem and a phase transition is established.
Some remarks on first passage of Levy processes, the American put and pasting principles
这篇文章的目的是，借助于波动恒等式，在Levy过程的第一通过时间和高于/低于固定水平的过冲的许多已知恒等式与Gerber和Shiu [Astin Bull.24（1994）195-220]，Boyarchenko和Levendorskii [Working paper series EERS 98/02（1998），未发表的手稿（1999年），SIAM J. Control Optim. 40（2002）1663-1696]，Chan [Original unpublished manuscripts（2000）]，Avram，Chan and Usabel [随机过程. 100（2002）75-107]，Mordecki [Finance Stoch. 6（2002）473-493]，Asmussen，Avram和Pistorius [随机过程. 109（2004）79-111]和Chesney和Jeanblanc [Appl.Math.Fin. 11（2004）207-225]的最优停止问题。此外，我们使民俗精确，并给出光滑粘贴发生在所考虑的问题的充要条件和充分条件。
