On the American option problem. (English) Zbl 1109.91028

Peskir, Goran

Math. Finance 15, No. 1, 169-181 (2005).

Summary: We show how the change-of-variable formula with local time on curves derived recently in G. Peskir [J. Theor. Probab. 18, No. 3, 499-535 (2005; Zbl 1085.60033)] 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.

MSC:

91G20	Derivative securities (option pricing, hedging, etc.)
60G40	Stopping times; optimal stopping problems; gambling theory

Keywords:

arbitrage-free price; optimal stopping; smooth fit; geometric Brownian motion; free-boundary problem; nonlinear integral equation; local time-space calculus; curved boundary

Citations:

Zbl 1085.60033

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