Optimal investment in the protection of a vulnerable biological resource
Date
2009-08-20T16:38:21Z
Authors
Reed, William J.
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Abstract
It is assumed that the probability of destruction of a biological asset by natural hazards can be reduced through investment in protection. Specifically a model, in which the hazard rate depends on both the age of the asset and the accumulated invested protection capital, is assumed. The protection capital is subject to depreciation through time and its effectiveness in reducing the hazard rate is subject to diminishing returns. It is shown how the investment schedule to maximize the expected net present value of the asset can be determined using the methods of deterministic optimal control, with the survival probability regarded as a state variable. The optimal investment pattern involves "bang-bang-singular" control. A numerical scheme for determining jointly the optimal investment policy and the optimal harvest (or replacement) age is outlined and a numerical example involving forest fire protection is given.
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Keywords
catastrophe, protection investment, hazard rate, optimal control, forest fire, pests, biological resources, technical reports (mathematics and statistics)