On a finite horizon starting and stopping problem with risk of abandonment

Boualem Djehiche, Said HamadÈne

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)523-543
Number of pages21
JournalInternational Journal of Theoretical and Applied Finance
Issue number4
StatePublished - Jun 2009


  • 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

ASJC Scopus subject areas

  • Finance
  • General Economics, Econometrics and Finance


Dive into the research topics of 'On a finite horizon starting and stopping problem with risk of abandonment'. Together they form a unique fingerprint.

Cite this