π options

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:120

Article

Guo, Xin²  Zervos, Mihail¹ 

[1] London Sch Econ, Dept Math, London WC2A 2AE, England

[2] UC Berkeley, Dept Ind Engn & Operat Res, Berkeley, CA 94720 USA

关键词: Optimal stopping;    Running maximum process;    Variational inequality;    Two dimensional free-boundary problem;    Separatrix;   

DOI  :  10.1016/j.spa.2010.02.008

来源: Elsevier

【 摘 要 】

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. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free