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ON THE AMERICAN OPTION PROBLEM
Author(s) -
Peskir Goran
Publication year - 2005
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.0960-1627.2005.00214.x
Subject(s) - optimal stopping , stopping time , mathematics , representation (politics) , variable (mathematics) , mathematical economics , nonlinear system , put option , boundary (topology) , economics , mathematical optimization , econometrics , mathematical analysis , actuarial science , statistics , physics , political science , quantum mechanics , politics , law
We show how the change‐of‐variable formula with local time on curves derived recently in Peskir (2002) can be used to prove that the optimal stopping boundary for the American put option can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premium representation. This settles the question raised in Myneni (1992) and dating back to McKean (1965).