Hysteretic regime switching diffusions and resource extraction

Moriarty, John and Evatt, Geoffrey W. and Johnson, Paul V. and Duck, Peter W. (2011) Hysteretic regime switching diffusions and resource extraction. [MIMS Preprint]

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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
Uncontrolled Keywords: Partial Differential Equations, Regime Switching Diffusion, Hysteresis, Hitting Probability.
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 39 Difference and functional equations
MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Ms Lucy van Russelt
Date Deposited: 18 Feb 2011
Last Modified: 08 Nov 2017 18:18
URI: https://eprints.maths.manchester.ac.uk/id/eprint/1583

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