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### Perpetual American options in incomplete markets : the infinitely divisible case

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Henderson, Vicky and Hobson, David (David G.).
(2008)
*Perpetual American options in incomplete markets : the infinitely divisible case.*
Quantitive Finance, Vol.8
(No.5).
pp. 461-469.
ISSN 1469-7688

**Full text not available from this repository.**

Official URL: http://dx.doi.org/10.1080/14697680701400986

## Abstract

We consider the exercise of a number of American options in an incomplete market. In this paper we are interested in the case where the options are infinitely divisible. We make the simplifying assumptions that the options have infinite maturity, and the holder has exponential utility. Our contribution is to solve this problem explicitly and we show that, except at the initial time when it may be advantageous to exercise a positive fraction of his holdings, it is never optimal for the holder to exercise a tranche of options. Instead, the process of option exercises is continuous; however, it is singular with respect to calendar time. Exercise takes place when the stock price reaches a convex boundary which we identify.

Item Type: | Journal Article |
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Subjects: | H Social Sciences > HB Economic Theory H Social Sciences > HG Finance Q Science > QA Mathematics |

Divisions: | Faculty of Science > Statistics |

Library of Congress Subject Headings (LCSH): | Options (Finance), Markets, Equilibrium (Economics), Distribution (Probability theory) |

Journal or Publication Title: | Quantitive Finance |

Publisher: | IOP Publishing |

ISSN: | 1469-7688 |

Date: | 2008 |

Volume: | Vol.8 |

Number: | No.5 |

Number of Pages: | 9 |

Page Range: | pp. 461-469 |

Identification Number: | 10.1080/14697680701400986 |

Status: | Peer Reviewed |

Publication Status: | Published |

Funder: | National Science Foundation (U.S.) (NSF), Engineering and Physical Sciences Research Council (EPSRC) |

Grant number: | DMI 0447990 (NSF) |

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URI: | http://wrap.warwick.ac.uk/id/eprint/29494 |

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