Free boundary and optimal stopping problems for American Asian options (Q928494)

The author considers a quite general financial model, possibly corresponding to degenerate partial differential equation, that includes Asian options and path-dependent volatility models as particular cases. A suitable functional setting is introduced and in this framework the existence and uniqueness of a strong solution to the free boundary and optimal stopping problems are proved. A Feynman-Kač-type theorem connects the free boundary and optimal stopping problems. The regularity properties of the solution are the following: the solution has weak second-order derivatives il \(L^p_{loc}\) for any \(p\geq 1\) and locally Hölder-continuous first-order derivatives. The framework is sufficiently general to include geometric Asian options with nonconstant volatility and recent path-dependent volatility models.