Journal of Applied Mathematics and Decision Sciences
Volume 6 (2002), Issue 1, Pages 51-70
Hedging entry and exit decisions: activating and deactivating
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Copyright © 2002 Laurent Gauthier. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract. Investment projects and businesses can be entered or exited at a cost,
and the theory of real option teaches us how to find optimal activity levels that should
trigger entry or exit. However, in practice, different managers or owners operate under
different constraints and might apply different thresholds to the same business. We are
interested in the hedging of the risk related to the cost of sub-optimal entry or exit.
We introduce a new class of derivative products that can hedge this risk. The pricing
of these derivatives involves the joint law of a Brownian excursion and its supremum,
which is calculated thanks to Bessel processes-related distribution laws.