Open AccessA STOCHASTIC FEEDBACK MODEL FOR OPTIMAL MANAGEMENT OF RENEWABLE RESOURCES
Author(s) -
Sandal Leif K.,
Steinshamn Stein Ivar
Publication year - 1997
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/j.1939-7445.1997.tb00209.x
Subject(s) - stock (firearms) , renewable resource , quadratic equation , optimal control , variable (mathematics) , control variable , maximum principle , mathematical optimization , stochastic control , stochastic modelling , state variable , function (biology) , yield (engineering) , stochastic process , mathematics , economics , computer science , mathematical economics , renewable energy , ecology , statistics , engineering , biology , mechanical engineering , mathematical analysis , physics , geometry , materials science , evolutionary biology , metallurgy , thermodynamics
Analytical expressions for optimal harvest of a renewable resource stock which is subject to a stochastic process are found. These expressions give the optimal harvest as an explicit feedback control law. All relations in the model, including the stochastic process, may be arbitrary functions of the state variable (stock). The objective function, however, is at most a quadratic function in the control variable (yield). A quadratic objective function includes the cases of downward sloping demand and increasing marginal costs which are the most common sources for nonlinearities in the economic part of the model. When it is assumed that there is a moratorium on harvest for stock sizes below a certain level (biological barrier), it is shown that the barrier requirements influence the optimal harvest paths throughout.