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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big SPECIAL DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Friday, February 18, 2000}
\centerline{Sequoia Hall Rm. 200}

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\centerline{\sl Hui Wang}
\centerline{\sl Columbia University}
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\centerline{\bf A Barrier Option of American Type}
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We obtain close-form expressions for the prices and optimal hedging
strategies of American put options in the presence of an "up-and-out"
barrier, both with and without constraints on the short-selling of stock.
The constrained case leads to an interesting stochastic optimization
problem of mixed optimal stopping/singular control type; this is reduced to
a variational inequality, which is then solved explicitly.

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