کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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1156062 | 958799 | 2010 | 27 صفحه PDF | دانلود رایگان |
We consider a discretionary stopping problem that arises in the context of pricing a class of perpetual American-type call options, which include the perpetual American, Russian and lookback-American call options as special cases. We solve this genuinely two-dimensional optimal stopping problem by means of an explicit construction of its value function. In particular, we fully characterise the free-boundary that provides the optimal strategy, and which involves the analysis of a highly nonlinear ordinary differential equation (ODE). In accordance with other optimal stopping problems involving a running maximum process that have been studied in the literature, it turns out that the associated variational inequality has an uncountable set of solutions that satisfy the so-called principle of smooth fit.
Journal: Stochastic Processes and their Applications - Volume 120, Issue 7, July 2010, Pages 1033–1059