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On a finite horizon starting and stopping problem with risk of abandonment
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0002-6608-0715
2009 (English)In: International Journal of Theoretical and Applied Finance, ISSN 0219-0249, Vol. 12, no 4, 523-543 p.Article in journal (Refereed) Published
Abstract [en]

We address the issue of finding a strategy to sustain structural profitability of an investment project, whose production activity depends on the market price of a number of underlying commodities. Depending on the fluctuating prices of these commodities, the activity will either continue until the project's profitability reaches a critical low level at which it is stopped and starts again when it becomes profitable. But, if the structural nonprofitability remains for a while, the investment project will face the risk to be abandoned or be definitely closed. We suggest a general probabilistic set up to model profitability as a function of the market price of a set of commodities, and find the related optimal strategy to sustain it, under the constraint that the project faces the abandonment risk when being nonprofitable under a fixed finite time interval. When the market price dynamics is described by a diffusion process, we show that the optimal strategy is related to viscosity solutions of a system of two variational inequalities with inter-connected obstacles.

Place, publisher, year, edition, pages
2009. Vol. 12, no 4, 523-543 p.
Keyword [en]
Abandonment risk, Backward stochastic differential equation, Optimal switching, Real options, Security design, Snell envelope, Stopping and starting, Stopping time, Variational inequalities, Viscosity solution of PDEs
National Category
URN: urn:nbn:se:kth:diva-59944DOI: 10.1142/S0219024909005312ScopusID: 2-s2.0-68149182289OAI: diva2:476766
QC 20120125Available from: 2012-01-12 Created: 2012-01-12 Last updated: 2012-01-25Bibliographically approved

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Djehiche, Boualem
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