## 2011.19: Hysteretic regime switching diffusions and resource extraction

2011.19:
John Moriarty, Geoffrey W. Evatt, Paul V. Johnson and Peter W. Duck
(2011)
*Hysteretic regime switching diffusions and resource
extraction.*

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## Abstract

We calculate the probability that an extraction project will be abandoned, directly from a real options model closely related the seminal work of Brennan and Schwartz (1985). We assume that the resource is extracted at two alternative rates, with a capital cost for switching, and with an option to abandon due to unsatisfactory market prices. The abandonment probability is expressed as a hitting probability for a regime switching diffusion with hysteresis, which is shown to be the unique solution of a system of coupled boundary value problems. Our work lends itself to use as a quantitative and easily interpreted measure of risk in the planning of extraction projects. Numerical results show that the abandonment probability may be non-monotone with respect to the volatility of the price process, in contrast with project valuations. In the one-dimensional stationary case, the stochastic process is a hysteretic system with noise in the sense of Freidlin et al. (2000), and we obtain a closed-form expression for the hitting or abandonment probability in this case.

Item Type: | MIMS Preprint |
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Uncontrolled Keywords: | Partial Differential Equations, Regime Switching Diffusion, Hysteresis, Hitting Probability. |

Subjects: | MSC 2000 > 39 Difference and functional equations MSC 2000 > 60 Probability theory and stochastic processes |

MIMS number: | 2011.19 |

Deposited By: | Ms Lucy van Russelt |

Deposited On: | 18 February 2011 |

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