English, Article edition: ON A FINITE HORIZON STARTING AND STOPPING PROBLEM WITH RISK OF ABANDONMENT BOUALEM DJEHICHE; SAID HAMADÃNE

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Physical Description
  • article
Language
  • English

Edition details

Title
  • ON A FINITE HORIZON STARTING AND STOPPING PROBLEM WITH RISK OF ABANDONMENT
Author
  • BOUALEM DJEHICHE
  • SAID HAMADÃNE
Physical Description
  • article
Notes
  • 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.
  • Real options, security design, backward stochastic differential equation, abandonment risk, Snell envelope, stopping time, stopping and starting, optimal switching, viscosity solution of PDEs, variational inequalities, 60G40, 93E20, 62P20, 91B99
  • RePEc:wsi:ijtafx:v:12:y:2009:i:04:p:523-543
Language
  • English
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