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Optimal investment-consumption problem with constraint
1. | School of Insurance, Central University Of Finance and Economics, Beijing 100081 |
2. | Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong |
3. | Department of Mathematics and Statistics, Curtin University, Perth, W.A. 6845 |
References:
[1] |
D. Applebeaum, "Levy Processes and Stochastic Calculus," $2^{nd}$ edition, Cambridge university Press, New York, 2009.
doi: 10.1017/CBO9780511809781. |
[2] |
J. M. Bismut, Conjugate convex functions in optimal stochastic control, Math. Anal. Appl., 44 (1974), 384-404.
doi: 10.1016/0022-247X(73)90066-8. |
[3] |
S. M. Chen, Z. F. Li and K. M. Li, Optimal investment-einsurance policy for an insurance company with VaR constraint, Insurance: Mathematics and Economics, 47 (2010), 144-153.
doi: 10.1016/j.insmatheco.2010.06.002. |
[4] |
J. C. Cox and C. F. Huang, Optimal consumption and portfolio policies when asset prices follow a diffusion process, J. Econom. Theory., 49 (1989), 33-83.
doi: 10.1016/0022-0531(89)90067-7. |
[5] |
J. C. Cox and C. F. Huang, A variational problem arising in financial economics, J. Math. Econom., 20 (1991), 465-487.
doi: 10.1016/0304-4068(91)90004-D. |
[6] |
D. Cuoco, Optimal consumption and equilibrium prices with portfolio constraints and stochastic income, J. Econom. Theory., 72 (1997), 33-73.
doi: 10.1006/jeth.1996.2207. |
[7] |
J. Cvitanic and I. Karatzas, Convex duality in constrained portfolio optimization, Ann. Appl. Probab., 2 (1992), 767-818.
doi: 10.1214/aoap/1177005576. |
[8] |
J. M. Harrison and D. Kreps, Martingales and arbitrage in multiperiod security markets, J. Econom. Theory., 20 (1979), 381-408.
doi: 10.1016/0022-0531(79)90043-7. |
[9] |
J. M. Harrison and S. R. Pliska, Martingales and stochastic integrals in the theory of continuous trading, Stochastic Process. Appl., 11 (1981), 215-260.
doi: 10.1016/0304-4149(81)90026-0. |
[10] |
H. He and N. D. Pearson, Consumption and portfolio policies with incomplete markets and short-sale constraints: The finite-dimensional case, Mathematical Finance, 1 (1991), 1-10.
doi: 10.1016/0022-0531(91)90123-L. |
[11] |
H. He and N. D. Pearson, Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite-dimensional case, J. Econom. Theory., 54 (1991), 259-304.
doi: 10.1016/0022-0531(91)90123-L. |
[12] |
I. Karatzas, J. P. Lehoczky and S. E. Shreve, Optimal portfolio and consumption decisions for a small investor on a finite horizon, SIAM J. Control Optim., 25 (1987), 1557-1586.
doi: 10.1137/0325086. |
[13] |
I. Karatzas, J. P. Lehoczky, S. E. Shreve and G. L. Xu, Martingale and duality methods for utility maximization in incomplete markets, Mathematical Finance, 15 (1991), 203-212.
doi: 10.1137/0329039. |
[14] |
D. Kramkov and W. Schachermayer, The asymptotic elasticity of utility functions and optimal investment in incomplete markets, Ann. Appl. Probab., 9 (1999), 904-950.
doi: 10.1214/aoap/1029962818. |
[15] |
V. L. Levin, Extreme problems with convex functionals that are lower-semicontinuous with respect to convergence in measure, Soviet math. Dokl., 16 (1976), 1384-1388. |
[16] |
J. Z. Liu, K. F. C. Yiu and K. L. Teo, Optimal portfolios with stress analysis and the effect of a CVaR constraint, Pac. J. Optim., 7 (2011), 83-95. |
[17] |
J. Z. Liu, L. H. Bai and K. F. C. Yiu, Optimal investment with a value-at-risk constraint, Journal of Industrial and Management Optimization, 8 (2012), 531-547.
doi: 10.3934/jimo.2012.8.531. |
[18] |
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, The Review of Economics and Statistics, 51 (1969), 247-257.
doi: 10.2307/1926560. |
[19] |
R. C. Merton, Optimal consumption and portfolio rules in a continuous-time model, J. Econom. Theory., 3 (1971), 373-413.
doi: 10.1016/0022-0531(71)90038-X. |
[20] |
T. A. Pirvu, Portfolio optimization under the Value-at-Risk constraint, Quantitative Finance, 7 (2007), 125-136.
doi: 10.1080/14697680701213868. |
[21] |
S. R. Pliska, A stochastic calculus model of continuous trading: Optimal portfolio, Math. Oper. Res., 11 (1986), 371-382.
doi: 10.1287/moor.11.2.371. |
[22] |
S. A. Ross, The arbitrage theory of capital asset pricing, J. Econom. Theory., 13 (1976), 341-360.
doi: 10.1016/0022-0531(76)90046-6. |
[23] |
K. F. C. Yiu, Optimal portfolio under a value-at-risk constraint, Journal of Economic Dynamics and Control, 28 (2004), 1317-1334.
doi: 10.1016/S0165-1889(03)00116-7. |
[24] |
K. F. C. Yiu, J. Z. Liu, T. K. Siu and W. C. Ching, Optimal portfolios with regime-switching and value-at-risk constraint, Automatica, 46 (2010), 1979-989.
doi: 10.1016/j.automatica.2010.02.027. |
show all references
References:
[1] |
D. Applebeaum, "Levy Processes and Stochastic Calculus," $2^{nd}$ edition, Cambridge university Press, New York, 2009.
doi: 10.1017/CBO9780511809781. |
[2] |
J. M. Bismut, Conjugate convex functions in optimal stochastic control, Math. Anal. Appl., 44 (1974), 384-404.
doi: 10.1016/0022-247X(73)90066-8. |
[3] |
S. M. Chen, Z. F. Li and K. M. Li, Optimal investment-einsurance policy for an insurance company with VaR constraint, Insurance: Mathematics and Economics, 47 (2010), 144-153.
doi: 10.1016/j.insmatheco.2010.06.002. |
[4] |
J. C. Cox and C. F. Huang, Optimal consumption and portfolio policies when asset prices follow a diffusion process, J. Econom. Theory., 49 (1989), 33-83.
doi: 10.1016/0022-0531(89)90067-7. |
[5] |
J. C. Cox and C. F. Huang, A variational problem arising in financial economics, J. Math. Econom., 20 (1991), 465-487.
doi: 10.1016/0304-4068(91)90004-D. |
[6] |
D. Cuoco, Optimal consumption and equilibrium prices with portfolio constraints and stochastic income, J. Econom. Theory., 72 (1997), 33-73.
doi: 10.1006/jeth.1996.2207. |
[7] |
J. Cvitanic and I. Karatzas, Convex duality in constrained portfolio optimization, Ann. Appl. Probab., 2 (1992), 767-818.
doi: 10.1214/aoap/1177005576. |
[8] |
J. M. Harrison and D. Kreps, Martingales and arbitrage in multiperiod security markets, J. Econom. Theory., 20 (1979), 381-408.
doi: 10.1016/0022-0531(79)90043-7. |
[9] |
J. M. Harrison and S. R. Pliska, Martingales and stochastic integrals in the theory of continuous trading, Stochastic Process. Appl., 11 (1981), 215-260.
doi: 10.1016/0304-4149(81)90026-0. |
[10] |
H. He and N. D. Pearson, Consumption and portfolio policies with incomplete markets and short-sale constraints: The finite-dimensional case, Mathematical Finance, 1 (1991), 1-10.
doi: 10.1016/0022-0531(91)90123-L. |
[11] |
H. He and N. D. Pearson, Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite-dimensional case, J. Econom. Theory., 54 (1991), 259-304.
doi: 10.1016/0022-0531(91)90123-L. |
[12] |
I. Karatzas, J. P. Lehoczky and S. E. Shreve, Optimal portfolio and consumption decisions for a small investor on a finite horizon, SIAM J. Control Optim., 25 (1987), 1557-1586.
doi: 10.1137/0325086. |
[13] |
I. Karatzas, J. P. Lehoczky, S. E. Shreve and G. L. Xu, Martingale and duality methods for utility maximization in incomplete markets, Mathematical Finance, 15 (1991), 203-212.
doi: 10.1137/0329039. |
[14] |
D. Kramkov and W. Schachermayer, The asymptotic elasticity of utility functions and optimal investment in incomplete markets, Ann. Appl. Probab., 9 (1999), 904-950.
doi: 10.1214/aoap/1029962818. |
[15] |
V. L. Levin, Extreme problems with convex functionals that are lower-semicontinuous with respect to convergence in measure, Soviet math. Dokl., 16 (1976), 1384-1388. |
[16] |
J. Z. Liu, K. F. C. Yiu and K. L. Teo, Optimal portfolios with stress analysis and the effect of a CVaR constraint, Pac. J. Optim., 7 (2011), 83-95. |
[17] |
J. Z. Liu, L. H. Bai and K. F. C. Yiu, Optimal investment with a value-at-risk constraint, Journal of Industrial and Management Optimization, 8 (2012), 531-547.
doi: 10.3934/jimo.2012.8.531. |
[18] |
R. C. Merton, Lifetime portfolio selection under uncertainty: The continuous-time case, The Review of Economics and Statistics, 51 (1969), 247-257.
doi: 10.2307/1926560. |
[19] |
R. C. Merton, Optimal consumption and portfolio rules in a continuous-time model, J. Econom. Theory., 3 (1971), 373-413.
doi: 10.1016/0022-0531(71)90038-X. |
[20] |
T. A. Pirvu, Portfolio optimization under the Value-at-Risk constraint, Quantitative Finance, 7 (2007), 125-136.
doi: 10.1080/14697680701213868. |
[21] |
S. R. Pliska, A stochastic calculus model of continuous trading: Optimal portfolio, Math. Oper. Res., 11 (1986), 371-382.
doi: 10.1287/moor.11.2.371. |
[22] |
S. A. Ross, The arbitrage theory of capital asset pricing, J. Econom. Theory., 13 (1976), 341-360.
doi: 10.1016/0022-0531(76)90046-6. |
[23] |
K. F. C. Yiu, Optimal portfolio under a value-at-risk constraint, Journal of Economic Dynamics and Control, 28 (2004), 1317-1334.
doi: 10.1016/S0165-1889(03)00116-7. |
[24] |
K. F. C. Yiu, J. Z. Liu, T. K. Siu and W. C. Ching, Optimal portfolios with regime-switching and value-at-risk constraint, Automatica, 46 (2010), 1979-989.
doi: 10.1016/j.automatica.2010.02.027. |
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