## Memorandum,

Oslo University, Department of Economics

# No 25/2014: The Effect of Small Intervention Costs on the Optimal Extraction of Dividends and Renewable Resources in a Jump-Diffusion Model

*Nils Chr. Framstad*
()

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Nils Chr. Framstad: Dept. of Economics, University of Oslo, Postal: Department of Economics, University of Oslo, P.O Box 1095 Blindern, N-0317 Oslo, Norway

**Abstract:** A risk-neutral agent optimizes extraction of dividends or renewable natural resources modelled by a jump-diffusion stock process, where the optimal strategy is characterized as the minimal intervention required to keep the stock process inside a given region. The introduction of a small fixed cost per intervention, is shown to induce a loss at worst of order, corresponding to a minimal intervention size of order, under suitable conditions; there are degenerate cases if purely discontinuous harvesting is optimal for the frictionless problem. If extraction is reversible, at cost between half and twice the extraction cost, the exponents are 1/2 and 1/4, agreeing with the effect of fixed costs in a consumption–portfolio optimization problem for a risk-averse agent.

**Keywords:**
Optimal stochastic control; resource extraction; dividend extraction; jump-diffusion model; transaction costs

**JEL-codes:**
D23; G11; Q20

26 pages, November 27, 2014

**Full text files**

memo-25-2014.pdf

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