A Barrier Option of American Type |
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| Authors: | I Karatzas H Wang |
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| Institution: | (1) Departments of Mathematics and Statistics, 619 Math. Bldg., Columbia University, New York, NY 10027, USA ik@math.columbia.edu , US;(2) Division of Applied Mathematics, 182 George Street, Room 223, Brown University, Box F, Providence, RI 02915, USA huiwang@cfm.brown.edu , US |
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| Abstract: | We obtain closed-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 a stochastic optimization
problem of mixed optimal stopping/singular control type. This is reduced to a variational inequality which is then solved explicitly in two qualitatively separate cases, according
to a certain compatibility condition among the market coefficients and the constraint.
Accepted 18 May 2000. Online publication 13 November 2000. |
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| Keywords: | , American option, Barrier option, Singular stochastic control, Optimal stopping, Variational inequality, Hedging,,,,,,Elastic boundary condition, Constrained portfolios, AMS Classification, Primary 93E20, 90A09, 60H30, Secondary 60G40, 60G44,,,,,,90A16, |
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