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Dynamic optimization models in finance: Some extensions to the framework, models, and computation
1. | Department of Mathematics & Statistics, University of Melbourne, Victoria 3010, Australia |
2. | Victoria University, P.O. Box 14428, Melbourne, Vic. 6001, Australia |
References:
[1] |
P. Brandimarte, Numerical Methods in Finance: A MATLAB-based introduction,, Second edition. Statistics in Practice. Wiley-Interscience [John Wiley & Sons], (2006).
doi: 10.1002/0470080493. |
[2] |
W. Brock, Sensitivity of optimal growth paths with respect to a change in target stocks,, Zeitchrift für National Ökonomie, 1 (1971), 73.
|
[3] |
B. D. Craven, Convergence of discrete approximations for constrained minimizatiion,, Journal of the Australian Mathematical Society, 36 (1994), 50.
doi: 10.1017/S0334270000010237. |
[4] |
B. D. Craven, Control and Optimization,, Chapman & Hall, (1995).
|
[5] |
B. D. Craven, Optimal control and invexity,, Computers and Mathematics with Applications, 35 (1998), 17.
doi: 10.1016/S0898-1221(98)00002-9. |
[6] |
B. D. Craven, Optimal control of an economic model with a small stochastic term,, Pacific Journal of Optimization, 1 (2005), 233.
|
[7] |
B. D. Craven, K. de Haas and J. Wettenhall, Computing optimal control,, Dynamics of Continuous, 4 (1988), 601.
|
[8] |
B. D. Craven and S. M. N. Islam, Computing optimal control on MATLAB: The scom package and economic growth models,, in Optimisation and Related Topics, 47 (1999), 61.
|
[9] |
B. D. Craven and S. M. N. Islam, Optimization in Economics and Finance,, Springer, (2005).
|
[10] |
K. Cuthbertson, Quantitative Financial Economics: Stocks, Bonds, and Foreign Exchange,, John Wiley, (1996). Google Scholar |
[11] |
B. Davis and D. Elzinga, The solution of an optimal control problem in financial modeling,, Operations Research, 19 (1971), 1419.
doi: 10.1287/opre.19.6.1419. |
[12] |
W. Diewert, Generalized Concavity and Economics,, in Generalized Concavity in Optimization and Economics, (1981).
|
[13] |
P. Dutta, On specifying the parameters of a development plan,, in Capital, (1993), 75. Google Scholar |
[14] |
K. Fox, J. K. Sengupta and E. Thorbecke, The Theory of Quantitative Economic Policy with Applications to Economic Growth,, Stabilization and Planning, (1973). Google Scholar |
[15] |
C. Goh and K. L. Teo, MISER: A FORTRAN program for solving optimal control problems,, Advances in Engineering Software, 10 (1988), 90.
doi: 10.1016/0141-1195(88)90005-8. |
[16] |
C. Gourieroux and J. Janiak, Financial Econometrics,, Princeton University Press, (2001).
doi: 10.7202/010560ar. |
[17] |
N. Hakansson, Optimal investment and consumption strategies under risk for a class of utility functions,, Econometrica, 38 (1970), 587.
doi: 10.2307/1912196. |
[18] |
G. Heal, Valuing the Future: Economic Theory and Sustainability,, Columbia University Press, (1998). Google Scholar |
[19] |
S. M. N. Islam and B. D. Craven, Computation of non-linear continuous capital growth models: Experiments with optimal control algorithms and computer programs,, Economic Modelling: The International Journal of Theoretical and Applied Papers on Economic Modelling 18 (2001), 18 (2001), 551. Google Scholar |
[20] |
S. M. N. Islam and B. D. Craven, Measuring Sustainable Growth,, in Governance and Social Responsibility, (2002). Google Scholar |
[21] |
K. Judd, Numerical Methods in Economics,, MIT Press, (1998).
|
[22] |
D. Leonard D. and N. V. Long, Optimal Control Theory and Static Optimization in Economics,, Cambridge University Press, (1992).
|
[23] |
R. Lucas, Asset prices in an exchange economy,, Econometrica, 46 (1978), 1429.
doi: 10.2307/1913837. |
[24] |
A. Malliaris and W. Brock, Stochastic Methods in Economics and Finance,, Elsevier Science, (1982).
|
[25] |
T. Mitra, Sensitivity of optimal programmes with respect to changes in target stocks: The case of irreversible investment,, Journal of Economic Theory, 29 (1983), 172.
doi: 10.1016/0022-0531(83)90128-X. |
[26] |
T. Mitra and D. Ray, Dynamic optimization on a non-convex feasible set: Some general resulots for non-emooth technologies,, Zeitchrift für National Ökonomie, 44 (1984), 151.
doi: 10.1007/BF01289475. |
[27] |
M. Ramon and A. Scott, (Ed.), Computational Methods for the Study of Dynamic Economies,, Oxford University Press, (1999). Google Scholar |
[28] |
A. L. Schwartz, Theory and implementation of numerical methods based on Runge-Kutta integration for solving optimal control problems,, Dissertation, (1989). Google Scholar |
[29] |
J. K. Sengupta and P. Fanchon, Control Theory Methods in Economics,, Kluwer Academic, (1997).
doi: 10.1007/978-1-4615-6285-6. |
[30] |
C. Tapiero, Applied Stochastic Models and Control for Insurance and Finance,, Kluwer Academic, (1998).
doi: 10.1007/978-1-4615-5823-1. |
[31] |
K. L. Teo, C. Goh and K. Wong, A Unified Computational Approach for Optimal Control Problems,, Pitman Monographs and Surveys in Pure and Applied Mathematics, (1991).
|
[32] |
G. Thompson and S. Thore, Computational Economics: Economic Modeling with Optimization Software,, (Chapters 21 to 22 and Appendices A&B), (1993). Google Scholar |
[33] |
R. Vickson and W. Ziemba, Stochastic Optimisation Models in Finance,, Academic Press, (1975). Google Scholar |
[34] |
S. Zenios, (Ed.), Financial Optimization,, Cambridge University Press, (1993). Google Scholar |
show all references
References:
[1] |
P. Brandimarte, Numerical Methods in Finance: A MATLAB-based introduction,, Second edition. Statistics in Practice. Wiley-Interscience [John Wiley & Sons], (2006).
doi: 10.1002/0470080493. |
[2] |
W. Brock, Sensitivity of optimal growth paths with respect to a change in target stocks,, Zeitchrift für National Ökonomie, 1 (1971), 73.
|
[3] |
B. D. Craven, Convergence of discrete approximations for constrained minimizatiion,, Journal of the Australian Mathematical Society, 36 (1994), 50.
doi: 10.1017/S0334270000010237. |
[4] |
B. D. Craven, Control and Optimization,, Chapman & Hall, (1995).
|
[5] |
B. D. Craven, Optimal control and invexity,, Computers and Mathematics with Applications, 35 (1998), 17.
doi: 10.1016/S0898-1221(98)00002-9. |
[6] |
B. D. Craven, Optimal control of an economic model with a small stochastic term,, Pacific Journal of Optimization, 1 (2005), 233.
|
[7] |
B. D. Craven, K. de Haas and J. Wettenhall, Computing optimal control,, Dynamics of Continuous, 4 (1988), 601.
|
[8] |
B. D. Craven and S. M. N. Islam, Computing optimal control on MATLAB: The scom package and economic growth models,, in Optimisation and Related Topics, 47 (1999), 61.
|
[9] |
B. D. Craven and S. M. N. Islam, Optimization in Economics and Finance,, Springer, (2005).
|
[10] |
K. Cuthbertson, Quantitative Financial Economics: Stocks, Bonds, and Foreign Exchange,, John Wiley, (1996). Google Scholar |
[11] |
B. Davis and D. Elzinga, The solution of an optimal control problem in financial modeling,, Operations Research, 19 (1971), 1419.
doi: 10.1287/opre.19.6.1419. |
[12] |
W. Diewert, Generalized Concavity and Economics,, in Generalized Concavity in Optimization and Economics, (1981).
|
[13] |
P. Dutta, On specifying the parameters of a development plan,, in Capital, (1993), 75. Google Scholar |
[14] |
K. Fox, J. K. Sengupta and E. Thorbecke, The Theory of Quantitative Economic Policy with Applications to Economic Growth,, Stabilization and Planning, (1973). Google Scholar |
[15] |
C. Goh and K. L. Teo, MISER: A FORTRAN program for solving optimal control problems,, Advances in Engineering Software, 10 (1988), 90.
doi: 10.1016/0141-1195(88)90005-8. |
[16] |
C. Gourieroux and J. Janiak, Financial Econometrics,, Princeton University Press, (2001).
doi: 10.7202/010560ar. |
[17] |
N. Hakansson, Optimal investment and consumption strategies under risk for a class of utility functions,, Econometrica, 38 (1970), 587.
doi: 10.2307/1912196. |
[18] |
G. Heal, Valuing the Future: Economic Theory and Sustainability,, Columbia University Press, (1998). Google Scholar |
[19] |
S. M. N. Islam and B. D. Craven, Computation of non-linear continuous capital growth models: Experiments with optimal control algorithms and computer programs,, Economic Modelling: The International Journal of Theoretical and Applied Papers on Economic Modelling 18 (2001), 18 (2001), 551. Google Scholar |
[20] |
S. M. N. Islam and B. D. Craven, Measuring Sustainable Growth,, in Governance and Social Responsibility, (2002). Google Scholar |
[21] |
K. Judd, Numerical Methods in Economics,, MIT Press, (1998).
|
[22] |
D. Leonard D. and N. V. Long, Optimal Control Theory and Static Optimization in Economics,, Cambridge University Press, (1992).
|
[23] |
R. Lucas, Asset prices in an exchange economy,, Econometrica, 46 (1978), 1429.
doi: 10.2307/1913837. |
[24] |
A. Malliaris and W. Brock, Stochastic Methods in Economics and Finance,, Elsevier Science, (1982).
|
[25] |
T. Mitra, Sensitivity of optimal programmes with respect to changes in target stocks: The case of irreversible investment,, Journal of Economic Theory, 29 (1983), 172.
doi: 10.1016/0022-0531(83)90128-X. |
[26] |
T. Mitra and D. Ray, Dynamic optimization on a non-convex feasible set: Some general resulots for non-emooth technologies,, Zeitchrift für National Ökonomie, 44 (1984), 151.
doi: 10.1007/BF01289475. |
[27] |
M. Ramon and A. Scott, (Ed.), Computational Methods for the Study of Dynamic Economies,, Oxford University Press, (1999). Google Scholar |
[28] |
A. L. Schwartz, Theory and implementation of numerical methods based on Runge-Kutta integration for solving optimal control problems,, Dissertation, (1989). Google Scholar |
[29] |
J. K. Sengupta and P. Fanchon, Control Theory Methods in Economics,, Kluwer Academic, (1997).
doi: 10.1007/978-1-4615-6285-6. |
[30] |
C. Tapiero, Applied Stochastic Models and Control for Insurance and Finance,, Kluwer Academic, (1998).
doi: 10.1007/978-1-4615-5823-1. |
[31] |
K. L. Teo, C. Goh and K. Wong, A Unified Computational Approach for Optimal Control Problems,, Pitman Monographs and Surveys in Pure and Applied Mathematics, (1991).
|
[32] |
G. Thompson and S. Thore, Computational Economics: Economic Modeling with Optimization Software,, (Chapters 21 to 22 and Appendices A&B), (1993). Google Scholar |
[33] |
R. Vickson and W. Ziemba, Stochastic Optimisation Models in Finance,, Academic Press, (1975). Google Scholar |
[34] |
S. Zenios, (Ed.), Financial Optimization,, Cambridge University Press, (1993). Google Scholar |
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