The effect of small intervention costs on the optimal extraction of dividends and renewable resources in a jump-diffusion model

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 Kappa2/3, corresponding to a minimal intervention size of order Kappa1/3, 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.