Abstract
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 language | English (US) |
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Pages (from-to) | 523-543 |
Number of pages | 21 |
Journal | International Journal of Theoretical and Applied Finance |
Volume | 12 |
Issue number | 4 |
DOIs | |
State | Published - Jun 2009 |
Keywords
- 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