On a finite horizon starting and stopping problem with risk of abandonment
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
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.
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
IdentifiersURN: urn:nbn:se:kth:diva-59944DOI: 10.1142/S0219024909005312ScopusID: 2-s2.0-68149182289OAI: oai:DiVA.org:kth-59944DiVA: diva2:476766
QC 201201252012-01-122012-01-122012-01-25Bibliographically approved