Continuous Extraction under Risk

Lohmander, P. (1986). Continuous Extraction under Risk. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-86-016

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Abstract

The problem of optimal intertemporal extraction (harvest) of a resource is investigated. The resource stock and the price (exogenous) are Markov processes. The expected present value of all future profits is maximized. The effects of increasing risk in the process increments in the future on the present optimal control (the present extraction level) are investigated.

It is proved that increasing risk in the increments of the stochastic price--and growth--processes may imply higher or lower optimal present extraction.

The resuits are dependent on: a) Autocorrelation and stationarity in the price process; b) The first three derivatives of the extraction cost function; c) The first three derivatives of the deterministic part of the growth process.

The effect of increasing risk in the process increments on the sign of the optimal change in the present extraction level can be unambiguously determined in severaI cases.

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