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Controllability of the cubic Schroedinger equation via a low-dimensional source term
Time-inconsistent optimal control problems and the equilibrium HJB equation
1. | Department of Mathematics, University of Central Florida, Orlando, FL 32816 |
References:
[1] |
S. Basak and G. Chabakauri, Dynamic mean-variance asset allocation,, Rev. Finan. Stud., 23 (2010), 2970.
doi: 10.1093/rfs/hhq028. |
[2] |
T. Björk and A. Murgoci, A general theory of Markovian time inconsistent stochasitic control problem,, working paper., (). Google Scholar |
[3] |
T. Björk, A. Murgoci and X. Y. Zhou, Mean varaiance portfolio optimization with state dependent risk aversion,, Math. Finance, (). Google Scholar |
[4] |
E. V. Böhm-Bawerk, "The Positive Theory of Capital,'', Books for Libraries Press, (1891). Google Scholar |
[5] |
A. Caplin and J. Leahy, The recursive approach to time inconsistency,, J. Econ. Theory, 131 (2006), 134.
doi: 10.1016/j.jet.2005.05.006. |
[6] |
I. Ekeland and A. Lazrak, The golden rule when preferences are time inconsistent,, Math. Finan. Econ., 4 (2010), 29.
|
[7] |
I. Ekeland and T. A. Pirvu, Investment and consumption without commitment,, Math. Finan. Econ., 2 (2008), 57.
|
[8] |
I. Ekeland, O. Mbodji and T. A. Pirvu, Time-consistent portfolio management,, SIAM J. Financial Math., 3 (2012), 1. Google Scholar |
[9] |
W. H. Fleming and H. M. Soner, "Controlled Markov Processes and Viscosity Solutions,'', 2nd edition, 25 (2006).
|
[10] |
A. Friedman, "Partial Differential Equations of Parabolic Type,'', Prentice Hall, (1964).
|
[11] |
S. M. Goldman, Consistent plans,, Review of Economic Studies, 47 (1980), 533. Google Scholar |
[12] |
S. R. Grenadier and N. Wang, Investment under uncertainty and time-inconsistent preferences,, J. Finan. Econ., 84 (2007), 2. Google Scholar |
[13] |
P. J.-J. Herings and K. I. M. Rohde, Time-inconsistent preferences in a general equilibrium model,, Econ. Theory, 29 (2006), 591.
doi: 10.1007/s00199-005-0020-3. |
[14] |
Y. Hu, H. Jin and X. Y. Zhou, Time-inconsistent stochastic linear-quadratic control,, , (2011). Google Scholar |
[15] |
D. Hume, "A Treatise of Human Nature,'', First edition, (1739). Google Scholar |
[16] |
W. S. Jevons, "Theory of Political Economy,'', McMillan, (1871). Google Scholar |
[17] |
L. Karp and I. H. Lee, Time-consistent policies,, J. Econ. Theory, 112 (2003), 353.
doi: 10.1016/S0022-0531(03)00067-X. |
[18] |
D. Laibson, Golden eggs and hyperbolic discounting,, Quarterly J. Econ., 112 (1997), 443.
doi: 10.1162/003355397555253. |
[19] |
J. Ma, P. Protter and J. Yong, Solving forward-backward stochastic differential equations explicitly-a four-step scheme,, Probab. Theory Related Fields, 98 (1994), 339.
doi: 10.1007/BF01192258. |
[20] |
J. Ma and J. Yong, "Forward-Backward Stochastic Differential Equations and Their Applications,'', Lecture Notes in Math., 1702 (1999).
|
[21] |
A. Malthus, An essay on the principle of population,, in, (1986), 2. Google Scholar |
[22] |
A. Marshall, "Principles of Economics,'', 1st ed., (1890). Google Scholar |
[23] |
J. Marin-Solano and J. Navas, Consumption and portfolio rules for time-inconsistent investors,, European J. Operational Research, 201 (2010), 860.
doi: 10.1016/j.ejor.2009.04.005. |
[24] |
J. Marin-Solano and E. V. Shevkoplyas, Non-constant discounting and differential games with random time horizon,, Automatica J. IFAC, 47 (2011), 2626.
doi: 10.1016/j.automatica.2011.09.010. |
[25] |
M. Miller and M. Salmon, Dynamic games and the time inconsistency of optimal policy in open economics,, The Economic Journal, 95 (1985), 124.
doi: 10.2307/2232876. |
[26] |
I. Palacios-Huerta, Time-inconsistent preferences in Adam Smith and Davis Hume,, History of Political Economy, 35 (2003), 241.
doi: 10.1215/00182702-35-2-241. |
[27] |
V. Pareto, "Manuel d'Économie Politique,'', Girard and Brieve, (1909). Google Scholar |
[28] |
B. Peleg and M. E. Yaari, On the existence of a consistent course of action when tastes are changing,, Review of Economic Studies, 40 (1973), 391. Google Scholar |
[29] |
R. A. Pollak, Consistent planning,, Review of Economic Studies, 35 (1968), 185.
doi: 10.2307/2296547. |
[30] |
A. Smith, "The Theory of Moral Sentiments,'', First edition, (1759). Google Scholar |
[31] |
R. H. Strotz, Myopia and inconsistency indynamic utility maximization,, Review of Econ. Studies, 23 (1955), 165.
doi: 10.2307/2295722. |
[32] |
L. Tesfatsion, Time inconsistency of benevolent government economics,, J. Public Economics, 31 (1986), 25.
doi: 10.1016/0047-2727(86)90070-8. |
[33] |
J. Yong, Backward stochastic Volterra integral equations and some related problems,, Stoch. Proc. Appl., 116 (2006), 779.
doi: 10.1016/j.spa.2006.01.005. |
[34] |
J. Yong, Well-posedness and regularity of backward stochastic Volterra integral equations,, Prob. Theory Rel. Fields, 142 (2008), 21.
doi: 10.1007/s00440-007-0098-6. |
[35] |
J. Yong, A deterministic linear quadratic time-inconsistent optimal control problem,, Math. Control Related Fields, 1 (2011), 83.
|
[36] |
J. Yong, Deterministic time-inconsistent optimal control problems-An essentially cooperative approach,, Acta Math. Appl. Sinica Engl. Ser., 28 (2012), 1.
|
[37] |
J. Yong and X. Y. Zhou, "Stochastic Controls. Hamiltonian Systems and HJB Equations,'', Applications of Mathematics (New York), 43 (1999).
|
show all references
References:
[1] |
S. Basak and G. Chabakauri, Dynamic mean-variance asset allocation,, Rev. Finan. Stud., 23 (2010), 2970.
doi: 10.1093/rfs/hhq028. |
[2] |
T. Björk and A. Murgoci, A general theory of Markovian time inconsistent stochasitic control problem,, working paper., (). Google Scholar |
[3] |
T. Björk, A. Murgoci and X. Y. Zhou, Mean varaiance portfolio optimization with state dependent risk aversion,, Math. Finance, (). Google Scholar |
[4] |
E. V. Böhm-Bawerk, "The Positive Theory of Capital,'', Books for Libraries Press, (1891). Google Scholar |
[5] |
A. Caplin and J. Leahy, The recursive approach to time inconsistency,, J. Econ. Theory, 131 (2006), 134.
doi: 10.1016/j.jet.2005.05.006. |
[6] |
I. Ekeland and A. Lazrak, The golden rule when preferences are time inconsistent,, Math. Finan. Econ., 4 (2010), 29.
|
[7] |
I. Ekeland and T. A. Pirvu, Investment and consumption without commitment,, Math. Finan. Econ., 2 (2008), 57.
|
[8] |
I. Ekeland, O. Mbodji and T. A. Pirvu, Time-consistent portfolio management,, SIAM J. Financial Math., 3 (2012), 1. Google Scholar |
[9] |
W. H. Fleming and H. M. Soner, "Controlled Markov Processes and Viscosity Solutions,'', 2nd edition, 25 (2006).
|
[10] |
A. Friedman, "Partial Differential Equations of Parabolic Type,'', Prentice Hall, (1964).
|
[11] |
S. M. Goldman, Consistent plans,, Review of Economic Studies, 47 (1980), 533. Google Scholar |
[12] |
S. R. Grenadier and N. Wang, Investment under uncertainty and time-inconsistent preferences,, J. Finan. Econ., 84 (2007), 2. Google Scholar |
[13] |
P. J.-J. Herings and K. I. M. Rohde, Time-inconsistent preferences in a general equilibrium model,, Econ. Theory, 29 (2006), 591.
doi: 10.1007/s00199-005-0020-3. |
[14] |
Y. Hu, H. Jin and X. Y. Zhou, Time-inconsistent stochastic linear-quadratic control,, , (2011). Google Scholar |
[15] |
D. Hume, "A Treatise of Human Nature,'', First edition, (1739). Google Scholar |
[16] |
W. S. Jevons, "Theory of Political Economy,'', McMillan, (1871). Google Scholar |
[17] |
L. Karp and I. H. Lee, Time-consistent policies,, J. Econ. Theory, 112 (2003), 353.
doi: 10.1016/S0022-0531(03)00067-X. |
[18] |
D. Laibson, Golden eggs and hyperbolic discounting,, Quarterly J. Econ., 112 (1997), 443.
doi: 10.1162/003355397555253. |
[19] |
J. Ma, P. Protter and J. Yong, Solving forward-backward stochastic differential equations explicitly-a four-step scheme,, Probab. Theory Related Fields, 98 (1994), 339.
doi: 10.1007/BF01192258. |
[20] |
J. Ma and J. Yong, "Forward-Backward Stochastic Differential Equations and Their Applications,'', Lecture Notes in Math., 1702 (1999).
|
[21] |
A. Malthus, An essay on the principle of population,, in, (1986), 2. Google Scholar |
[22] |
A. Marshall, "Principles of Economics,'', 1st ed., (1890). Google Scholar |
[23] |
J. Marin-Solano and J. Navas, Consumption and portfolio rules for time-inconsistent investors,, European J. Operational Research, 201 (2010), 860.
doi: 10.1016/j.ejor.2009.04.005. |
[24] |
J. Marin-Solano and E. V. Shevkoplyas, Non-constant discounting and differential games with random time horizon,, Automatica J. IFAC, 47 (2011), 2626.
doi: 10.1016/j.automatica.2011.09.010. |
[25] |
M. Miller and M. Salmon, Dynamic games and the time inconsistency of optimal policy in open economics,, The Economic Journal, 95 (1985), 124.
doi: 10.2307/2232876. |
[26] |
I. Palacios-Huerta, Time-inconsistent preferences in Adam Smith and Davis Hume,, History of Political Economy, 35 (2003), 241.
doi: 10.1215/00182702-35-2-241. |
[27] |
V. Pareto, "Manuel d'Économie Politique,'', Girard and Brieve, (1909). Google Scholar |
[28] |
B. Peleg and M. E. Yaari, On the existence of a consistent course of action when tastes are changing,, Review of Economic Studies, 40 (1973), 391. Google Scholar |
[29] |
R. A. Pollak, Consistent planning,, Review of Economic Studies, 35 (1968), 185.
doi: 10.2307/2296547. |
[30] |
A. Smith, "The Theory of Moral Sentiments,'', First edition, (1759). Google Scholar |
[31] |
R. H. Strotz, Myopia and inconsistency indynamic utility maximization,, Review of Econ. Studies, 23 (1955), 165.
doi: 10.2307/2295722. |
[32] |
L. Tesfatsion, Time inconsistency of benevolent government economics,, J. Public Economics, 31 (1986), 25.
doi: 10.1016/0047-2727(86)90070-8. |
[33] |
J. Yong, Backward stochastic Volterra integral equations and some related problems,, Stoch. Proc. Appl., 116 (2006), 779.
doi: 10.1016/j.spa.2006.01.005. |
[34] |
J. Yong, Well-posedness and regularity of backward stochastic Volterra integral equations,, Prob. Theory Rel. Fields, 142 (2008), 21.
doi: 10.1007/s00440-007-0098-6. |
[35] |
J. Yong, A deterministic linear quadratic time-inconsistent optimal control problem,, Math. Control Related Fields, 1 (2011), 83.
|
[36] |
J. Yong, Deterministic time-inconsistent optimal control problems-An essentially cooperative approach,, Acta Math. Appl. Sinica Engl. Ser., 28 (2012), 1.
|
[37] |
J. Yong and X. Y. Zhou, "Stochastic Controls. Hamiltonian Systems and HJB Equations,'', Applications of Mathematics (New York), 43 (1999).
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