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Optimal harvesting and planting control in stochastic logistic population models
1.  Department of Economics, Matsuyama University, Matsuyama 7908578, Japan 
References:
[1] 
L. H. R. Alvarez and L. A. Shepp, Optimal harvesting of stochastically fluctuating populations, J. Math. Biol., 37 (1998), 155177. doi: 10.1007/s002850050124. 
[2] 
F. H. Clarke, "Optimizationand Nonsmooth Analysis," Canadian Mathematical Society Series of Monographs and Advanced Texts., A WileyInterscience Publication, John Wiley & Sons, Inc., New York, 1983. 
[3] 
M. G. Crandall, H. Ishii and P.L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.), 27 (1992), 167. doi: 10.1090/S027309791992002665. 
[4] 
W. H. Fleming and H. M. Soner, "Controlled Markov Processes and Viscosity Solutions," Applications of Mathematics (New York), 25, SpringerVerlag, New York, 1993. 
[5] 
N. Ikeda and S. Watanabe, "Stochastic Differential Equations and Diffusion Processes," NorthHolland Mathematical Library, 24, NorthHolland Publishing Co., AmsterdamNew York; Kodansha, Ltd., Tokyo, 1981. 
[6] 
I. Karatzas and S. E. Shreve, "Brownian Motion and Stochastic Calculus," Second edition, Graduate Texts in Mathematics, 113, SpringerVerlag, New York, 1991. 
[7] 
P.L. Lions and A.S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math., 37 (1984), 511537. doi: 10.1002/cpa.3160370408. 
[8] 
H. Morimoto, "Stochastic Control and Mathematical Modeling: Applications in Economics," Encyclopedia of Mathematics and its Applications, 131, Cambridge University Press, Cambridge, 2010. 
[9] 
H. Morimoto, A singular control problem with discretionary stopping for geometric Brownian motions, SIAM J. Control Optim., 48 (2010), 37813804. doi: 10.1137/080734856. 
[10] 
S. P. Sethi and M. I. Taksar, Optimal financing of a corporation subject to random returns, Math. Finance, 12 (2002), 155172. doi: 10.1111/14679965.t01202002. 
[11] 
S. E. Shreve, J. P. Lehoczky and D. P. Gaver, Optimal consumption for general diffusions with absorbing and reflecting barriers, SIAM J. Control Optim., 22 (1984), 5575. doi: 10.1137/0322005. 
show all references
References:
[1] 
L. H. R. Alvarez and L. A. Shepp, Optimal harvesting of stochastically fluctuating populations, J. Math. Biol., 37 (1998), 155177. doi: 10.1007/s002850050124. 
[2] 
F. H. Clarke, "Optimizationand Nonsmooth Analysis," Canadian Mathematical Society Series of Monographs and Advanced Texts., A WileyInterscience Publication, John Wiley & Sons, Inc., New York, 1983. 
[3] 
M. G. Crandall, H. Ishii and P.L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.), 27 (1992), 167. doi: 10.1090/S027309791992002665. 
[4] 
W. H. Fleming and H. M. Soner, "Controlled Markov Processes and Viscosity Solutions," Applications of Mathematics (New York), 25, SpringerVerlag, New York, 1993. 
[5] 
N. Ikeda and S. Watanabe, "Stochastic Differential Equations and Diffusion Processes," NorthHolland Mathematical Library, 24, NorthHolland Publishing Co., AmsterdamNew York; Kodansha, Ltd., Tokyo, 1981. 
[6] 
I. Karatzas and S. E. Shreve, "Brownian Motion and Stochastic Calculus," Second edition, Graduate Texts in Mathematics, 113, SpringerVerlag, New York, 1991. 
[7] 
P.L. Lions and A.S. Sznitman, Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math., 37 (1984), 511537. doi: 10.1002/cpa.3160370408. 
[8] 
H. Morimoto, "Stochastic Control and Mathematical Modeling: Applications in Economics," Encyclopedia of Mathematics and its Applications, 131, Cambridge University Press, Cambridge, 2010. 
[9] 
H. Morimoto, A singular control problem with discretionary stopping for geometric Brownian motions, SIAM J. Control Optim., 48 (2010), 37813804. doi: 10.1137/080734856. 
[10] 
S. P. Sethi and M. I. Taksar, Optimal financing of a corporation subject to random returns, Math. Finance, 12 (2002), 155172. doi: 10.1111/14679965.t01202002. 
[11] 
S. E. Shreve, J. P. Lehoczky and D. P. Gaver, Optimal consumption for general diffusions with absorbing and reflecting barriers, SIAM J. Control Optim., 22 (1984), 5575. doi: 10.1137/0322005. 
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