Optimal Environmental Management in the Presence of Irreversibilities |
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| Affiliation: | 1. School of Science, Systems Analysis Laboratory, Aalto University, P.O. Box 11100, 00076, Espoo, Finland.;1. Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Koom 32511, Egypt;2. Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk, Cairo, Egypt;3. Department of Physics and Engineering Mathematics, Higher Institute of Engineering and Technology, Tanta, Egypt;4. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762-7500, USA;5. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;6. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;7. Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok University, 66100 Yozgat, Turkey;8. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan 430212, People''s Republic of China;9. Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar;1. Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey;2. Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran;3. School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan, 430212, PR China;4. Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P.O. Box 12, 23000 Annaba, Algeria;5. Department of Mathematics, Faculty of Science, King Khalid University, PO Box 9004, Abha 61413, Saudi Arabia;6. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;1. Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt;2. Department of Engineering Mathematics and Physics, Higher Institute of Engineering, El-Shorouk, Cairo, Egypt;3. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762-7500, USA;4. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;5. Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Shosse, Moscow 115409, Russian Federation;6. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South Africa;7. Department of Mathematics, Faculty of Arts and Sciences, Near East University, 99138 Nicosia, Cyprus;8. Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar |
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| Abstract: | We consider an environment of a fixed size that can be converted to another use. This conversion can be made in steps, but it is irreversible. The future benefits (per unit) from the original use, and from the alternative use, follow a diffusion process. For a fairly general case, we show that the value function must be the unique (viscosity) solution to the associated Hamilton-Jacobi-Bellman equation. We also exhibit several properties of the solution for the case of constant relative risk aversion between 0 and 1, and a log-linear diffusion for the benefits. Journal of Economic Literature Classification Numbers: C61, D90, Q30. |
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