## 2007.37: The Russian option: Finite horizon

2007.37:
Goran Peskir
(2005)
*The Russian option: Finite horizon.*
Finance and Stochastics, 9 (2).
pp. 251-267.
ISSN 1432-1122

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DOI: 10.1007/s00780-004-0133-8

## Abstract

We show that the optimal stopping boundary for the Russian option with finite horizon can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premium representation (an explicit formula for the arbitrage-free price in terms of the optimal stopping boundary having a clear economic interpretation). The results obtained stand in a complete parallel with the best known results on the American put option with finite horizon. The key argument in the proof relies upon a local time-space formula.

Item Type: | Article |
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Uncontrolled Keywords: | Russian option - finite horizon - arbitrage-free price - optimal stopping - smooth-fit - geometric Brownian motion - free-boundary problem - nonlinear integral equation - local time-space calculus - curved boundary |

Subjects: | MSC 2000 > 35 Partial differential equations MSC 2000 > 45 Integral equations MSC 2000 > 60 Probability theory and stochastic processes MSC 2000 > 91 Game theory, economics, social and behavioral sciences |

MIMS number: | 2007.37 |

Deposited By: | Miss Louise Stait |

Deposited On: | 29 March 2007 |

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