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Applied Mathematics and Optimization

, Volume 42, Issue 3, pp 259–279 | Cite as

A Barrier Option of American Type

  • I. Karatzas
  • H. Wang

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.

Key words. 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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Copyright information

© Springer-Verlag New York Inc. 2000

Authors and Affiliations

  • I. Karatzas
    • 1
  • H. Wang
    • 2
  1. 1.Departments of Mathematics and Statistics, 619 Math. Bldg., Columbia University, New York, NY 10027, USA ik@math.columbia.edu US
  2. 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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