
-
Previous Article
Bargaining equilibrium in a two-echelon supply chain with a capital-constrained retailer
- JIMO Home
- This Issue
-
Next Article
An adaptively regularized sequential quadratic programming method for equality constrained optimization
How's the performance of the optimized portfolios by safety-first rules: Theory with empirical comparisons
1. | Faculty of Business, Ningbo University, Ningbo 315211, China |
2. | Southampton Statistical Sciences Research Institute, and Mathematical Sciences, University of Southampton, SO17 1BJ, UK |
Safety-first (SF) rules have been increasingly useful in particular for construction of optimal portfolios related to pension and other social insurance funds. How's the performance of the optimal portfolios constructed by different SF rules is an interesting practical question but yet less investigated theoretically. In this paper, we therefore analytically investigate the properties of the risky portfolios constructed by the three popular SF rules, denoted by the RSF, TSF and KSF, which are suggested and developed by A. D. Roy, L. G. Telser and S. Kataoka, respectively. Using Sharpe ratio as a measure of portfolio performance, we theoretically derive that the performance of an optimal portfolio constructed by the KSF approach depends on an acceptable level of extreme risk tolerance. The unique solution where the performance of the KSF portfolio is the same as that of the other two SF portfolios is found. By this we interestingly find that except this special case, under the finite optimal portfolios existent, the KSF portfolio always dominates the TSF portfolio in terms of the Sharpe ratio. In addition, in some market scenarios, even when the RSF and TSF portfolios do not exist in finite forms, the KSF rule can still apply to get a finite optimal portfolio. Moreover, in comparison with the RSF rule, a series of finite KSF portfolios can be interestingly constructed with their Sharpe ratios approaching to the maximum Sharpe ratio, which however cannot be reached by any corresponding finite RSF portfolio. Numerical comparisons of these rules by using a set of real data are further empirically demonstrated.
References:
[1] |
V. S. Bawa,
Safety-first, stochastic dominance, and optimal portfolio choice, Journal of Financial and Quantitative Analysis, 13 (1978), 255-271.
doi: 10.2307/2330386. |
[2] |
T. Bodnar and T. Zabolotskyy,
How risky is the optimal portfolio which maximizes the sharpe ratio?, Asta Advances in Statistical Analysis, 101 (2017), 1-28.
doi: 10.1007/s10182-016-0270-3. |
[3] |
Y. Ding and B. Zhang,
Risky asset pricing based on safety first fund management, Quantitative Finance, 9 (2009a), 353-361.
doi: 10.1080/14697680802392488. |
[4] |
Y. Ding and B. Zhang,
Optimal portfolio of safety-first models, Journal of Statistical Planning and Inference, 139 (2009b), 2952-2962.
doi: 10.1016/j.jspi.2009.01.018. |
[5] |
Y. Ding and Z. Lu,
The optimal portfolios based on a modified safety-first rule with risk-free saving, Journal of Industrial and Management Optimization, 12 (2016), 83-102.
doi: 10.3934/jimo.2016.12.83. |
[6] |
R. B. Durand, H. Jafarpour, C. Kluppelberg and R. Maller, Maximize the Sharpe Ratio and Minimize a VaR, The Journal of Wealth Management, 13 (2010), 91-102. Google Scholar |
[7] |
M. Engels, Portfolio Optimization: Beyond Markowitz, Master's thesis, Leiden University, Netherlands, 2004. Google Scholar |
[8] |
N. Gressis and W. A. Remaley, Comment: ``Safety first – an expected utility principle", Jounal of Financial and Quantitative Analysis, 9 (1974), 1057-1061. Google Scholar |
[9] |
H. Hagigi and B. Kluger, Assessing return and risk of pension funds–portfolios by the Telser safety-first approach, Journal of Business Finance and Accounting, 14 (1987), 241-253. Google Scholar |
[10] |
M. R. Haley and M. K. McGee, Tilting safety first and the Sharpe portfolio, Finance Research Letters, 3 (2006), 173-180. Google Scholar |
[11] |
S. Kataoka,
A stochastic programming model, Econometrica, 31 (1963), 181-196.
doi: 10.2307/1910956. |
[12] |
H. Levy and M. Sarnat, Safety first–an expected utility principle, Journal of Financial and Quantitative Analysis, 7 (1972), 1829-1834. Google Scholar |
[13] |
Z. F. Li and G. J. Chen, Some discussions on Telser's safety-first model for portfolio selection (in Chinese), Theory and Practice of System Engineering, 36 (2005), 8-14. Google Scholar |
[14] |
Z. F. Li, J. Yao and D. Li,
Behavior patterns of investment strategies under Roy's safety-first principle, The Quarterly Review of Economics and Finance, 50 (2010), 167-179.
doi: 10.1016/j.qref.2009.11.004. |
[15] |
R. A. Maller and D. A. Turkington,
New light on the portfolio allocation problem, Mathematical Methods of Operational Research, 56 (2002), 501-511.
doi: 10.1007/s001860200211. |
[16] |
H. Markowitz,
Portfolio selection, Journal of Finance, 7 (1952), 77-91.
|
[17] |
V. I. Norkin and S. V. Boyko,
Safety-first portfolio selection, Cybernetics and Systems Analysis, 48 (2012), 180-191.
doi: 10.1007/s10559-012-9396-9. |
[18] |
Y. Okhrin and W. Schmid,
Distributional properties of portfolio weights, Journal of Econometrics, 134 (2006), 235-256.
doi: 10.1016/j.jeconom.2005.06.022. |
[19] |
L. S. Ortobelli and S. T. Rachev,
Safety-first analysis and stable paretian approach to portfolio choice theory, Mathematical and Computer Modelling, 34 (2001), 1037-1072.
doi: 10.1016/S0895-7177(01)00116-9. |
[20] |
D. H. Pyle and S. J. Turnovsky, Safety-first and expected utility maximization in mean-standard deviation portfolio analysis, The Review of Economics and Statistics, 52 (1970), 75-81. Google Scholar |
[21] |
A. D. Roy,
Safety-first and the holding of assets, Econometrica, 20 (1952), 431-449.
doi: 10.2307/1907413. |
[22] |
W. F. Sharpe,
The Sharpe Ratio, Journal of Portfolio Management, 21 (1994), 49-58.
doi: 10.3905/jpm.1994.409501. |
[23] |
L. G. Telser,
Safety first and hedging, Review of Economic Studies, 23 (1955), 1-16.
doi: 10.2307/2296146. |
[24] |
S. Wang and Y. Xia, Portfolio Selection and Asset Pricing, Springer-Verlag, Berlin Heidelberg New York, Printed in Germany, 2002.
doi: 10.1007/978-3-642-55934-1. |
show all references
References:
[1] |
V. S. Bawa,
Safety-first, stochastic dominance, and optimal portfolio choice, Journal of Financial and Quantitative Analysis, 13 (1978), 255-271.
doi: 10.2307/2330386. |
[2] |
T. Bodnar and T. Zabolotskyy,
How risky is the optimal portfolio which maximizes the sharpe ratio?, Asta Advances in Statistical Analysis, 101 (2017), 1-28.
doi: 10.1007/s10182-016-0270-3. |
[3] |
Y. Ding and B. Zhang,
Risky asset pricing based on safety first fund management, Quantitative Finance, 9 (2009a), 353-361.
doi: 10.1080/14697680802392488. |
[4] |
Y. Ding and B. Zhang,
Optimal portfolio of safety-first models, Journal of Statistical Planning and Inference, 139 (2009b), 2952-2962.
doi: 10.1016/j.jspi.2009.01.018. |
[5] |
Y. Ding and Z. Lu,
The optimal portfolios based on a modified safety-first rule with risk-free saving, Journal of Industrial and Management Optimization, 12 (2016), 83-102.
doi: 10.3934/jimo.2016.12.83. |
[6] |
R. B. Durand, H. Jafarpour, C. Kluppelberg and R. Maller, Maximize the Sharpe Ratio and Minimize a VaR, The Journal of Wealth Management, 13 (2010), 91-102. Google Scholar |
[7] |
M. Engels, Portfolio Optimization: Beyond Markowitz, Master's thesis, Leiden University, Netherlands, 2004. Google Scholar |
[8] |
N. Gressis and W. A. Remaley, Comment: ``Safety first – an expected utility principle", Jounal of Financial and Quantitative Analysis, 9 (1974), 1057-1061. Google Scholar |
[9] |
H. Hagigi and B. Kluger, Assessing return and risk of pension funds–portfolios by the Telser safety-first approach, Journal of Business Finance and Accounting, 14 (1987), 241-253. Google Scholar |
[10] |
M. R. Haley and M. K. McGee, Tilting safety first and the Sharpe portfolio, Finance Research Letters, 3 (2006), 173-180. Google Scholar |
[11] |
S. Kataoka,
A stochastic programming model, Econometrica, 31 (1963), 181-196.
doi: 10.2307/1910956. |
[12] |
H. Levy and M. Sarnat, Safety first–an expected utility principle, Journal of Financial and Quantitative Analysis, 7 (1972), 1829-1834. Google Scholar |
[13] |
Z. F. Li and G. J. Chen, Some discussions on Telser's safety-first model for portfolio selection (in Chinese), Theory and Practice of System Engineering, 36 (2005), 8-14. Google Scholar |
[14] |
Z. F. Li, J. Yao and D. Li,
Behavior patterns of investment strategies under Roy's safety-first principle, The Quarterly Review of Economics and Finance, 50 (2010), 167-179.
doi: 10.1016/j.qref.2009.11.004. |
[15] |
R. A. Maller and D. A. Turkington,
New light on the portfolio allocation problem, Mathematical Methods of Operational Research, 56 (2002), 501-511.
doi: 10.1007/s001860200211. |
[16] |
H. Markowitz,
Portfolio selection, Journal of Finance, 7 (1952), 77-91.
|
[17] |
V. I. Norkin and S. V. Boyko,
Safety-first portfolio selection, Cybernetics and Systems Analysis, 48 (2012), 180-191.
doi: 10.1007/s10559-012-9396-9. |
[18] |
Y. Okhrin and W. Schmid,
Distributional properties of portfolio weights, Journal of Econometrics, 134 (2006), 235-256.
doi: 10.1016/j.jeconom.2005.06.022. |
[19] |
L. S. Ortobelli and S. T. Rachev,
Safety-first analysis and stable paretian approach to portfolio choice theory, Mathematical and Computer Modelling, 34 (2001), 1037-1072.
doi: 10.1016/S0895-7177(01)00116-9. |
[20] |
D. H. Pyle and S. J. Turnovsky, Safety-first and expected utility maximization in mean-standard deviation portfolio analysis, The Review of Economics and Statistics, 52 (1970), 75-81. Google Scholar |
[21] |
A. D. Roy,
Safety-first and the holding of assets, Econometrica, 20 (1952), 431-449.
doi: 10.2307/1907413. |
[22] |
W. F. Sharpe,
The Sharpe Ratio, Journal of Portfolio Management, 21 (1994), 49-58.
doi: 10.3905/jpm.1994.409501. |
[23] |
L. G. Telser,
Safety first and hedging, Review of Economic Studies, 23 (1955), 1-16.
doi: 10.2307/2296146. |
[24] |
S. Wang and Y. Xia, Portfolio Selection and Asset Pricing, Springer-Verlag, Berlin Heidelberg New York, Printed in Germany, 2002.
doi: 10.1007/978-3-642-55934-1. |





Covariance | 1B0010 | 1B0011 | 1B0006 | Returns |
1B0010 | 0.00863 | 0.00657 | 0.00830 | 0.00497 |
1B0011 | 0.00657 | 0.00609 | 0.00648 | 0.01214 |
1B0006 | 0.00830 | 0.00648 | 0.01390 | 0.00613 |
Covariance | 1B0010 | 1B0011 | 1B0006 | Returns |
1B0010 | 0.00863 | 0.00657 | 0.00830 | 0.00497 |
1B0011 | 0.00657 | 0.00609 | 0.00648 | 0.01214 |
1B0006 | 0.00830 | 0.00648 | 0.01390 | 0.00613 |
Panel | Rule | ||||||
RSF | 0.40512 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
1 | TSF | 0.40512 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 |
KSF | 0.40512 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
RSF | 0.41019 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
2 | TSF | 0.41297 | 0.41000 | -4.95741 | 5.94221 | 0.01520 | 0.22754 |
KSF | 0.41000 | 0.40532 | -2.83436 | 3.82477 | 0.00959 | 0.23960 | |
RSF | 0.41778 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
3 | TSF | 0.42074 | 0.41650 | -8.91672 | 9.89105 | 0.02567 | 0.21086 |
KSF | 0.41650 | 0.40657 | -3.51776 | 4.50637 | 0.01139 | 0.23638 | |
RSF | 0.42255 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
4 | TSF | 0.42393 | 0.42000 | -13.26792 | 14.23075 | 0.03718 | 0.20189 |
KSF | 0.42000 | 0.40813 | -4.17332 | 5.16010 | 0.01313 | 0.23235 | |
RSF | 0.11226 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
5 | TSF | N | 0.05000 | N | N | N | N |
KSF | 0.05000 | 0.42963 | -0.52073 | 1.51727 | 0.00347 | 0.17730 | |
RSF | 0.20922 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
6 | TSF | N | 0.15000 | N | N | N | N |
KSF | 0.15000 | 0.42565 | -0.64983 | 1.64602 | 0.00381 | 0.18745 | |
RSF | 0.40016 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
7 | TSF | N | 0.35000 | N | N | N | N |
KSF | 0.35000 | 0.41119 | -1.33611 | 2.33049 | 0.00562 | 0.22449 | |
RSF | 0.43132 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
8 | TSF | 0.42500 | 0.41307 | -6.47843 | 7.45921 | 0.01922 | 0.21966 |
KSF | 0.42500 | 0.41307 | -6.47843 | 7.45921 | 0.01922 | 0.21966 | |
RSF | 0.32258 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
9 | TSF | 0.38805 | 0.41650 | -8.91672 | 9.89105 | 0.02567 | 0.21086 |
KSF | 0.30000 | 0.41650 | -1.01839 | 2.01361 | 0.00478 | 0.21086 | |
RSF | 0.24886 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
10 | TSF | 0.40088 | 0.42330 | -22.61759 | 23.55569 | 0.06190 | 0.19346 |
KSF | 0.20000 | 0.42330 | -0.73281 | 1.72878 | 0.00403 | 0.19346 | |
RSF | 0.16529 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
11 | TSF | 0.42240 | 0.42768 | -160.68449 | 161.25747 | 0.42702 | 0.18229 |
KSF | 0.10000 | 0.42768 | -0.58263 | 1.57900 | 0.00363 | 0.18229 |
Panel | Rule | ||||||
RSF | 0.40512 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
1 | TSF | 0.40512 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 |
KSF | 0.40512 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
RSF | 0.41019 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
2 | TSF | 0.41297 | 0.41000 | -4.95741 | 5.94221 | 0.01520 | 0.22754 |
KSF | 0.41000 | 0.40532 | -2.83436 | 3.82477 | 0.00959 | 0.23960 | |
RSF | 0.41778 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
3 | TSF | 0.42074 | 0.41650 | -8.91672 | 9.89105 | 0.02567 | 0.21086 |
KSF | 0.41650 | 0.40657 | -3.51776 | 4.50637 | 0.01139 | 0.23638 | |
RSF | 0.42255 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
4 | TSF | 0.42393 | 0.42000 | -13.26792 | 14.23075 | 0.03718 | 0.20189 |
KSF | 0.42000 | 0.40813 | -4.17332 | 5.16010 | 0.01313 | 0.23235 | |
RSF | 0.11226 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
5 | TSF | N | 0.05000 | N | N | N | N |
KSF | 0.05000 | 0.42963 | -0.52073 | 1.51727 | 0.00347 | 0.17730 | |
RSF | 0.20922 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
6 | TSF | N | 0.15000 | N | N | N | N |
KSF | 0.15000 | 0.42565 | -0.64983 | 1.64602 | 0.00381 | 0.18745 | |
RSF | 0.40016 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
7 | TSF | N | 0.35000 | N | N | N | N |
KSF | 0.35000 | 0.41119 | -1.33611 | 2.33049 | 0.00562 | 0.22449 | |
RSF | 0.43132 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
8 | TSF | 0.42500 | 0.41307 | -6.47843 | 7.45921 | 0.01922 | 0.21966 |
KSF | 0.42500 | 0.41307 | -6.47843 | 7.45921 | 0.01922 | 0.21966 | |
RSF | 0.32258 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
9 | TSF | 0.38805 | 0.41650 | -8.91672 | 9.89105 | 0.02567 | 0.21086 |
KSF | 0.30000 | 0.41650 | -1.01839 | 2.01361 | 0.00478 | 0.21086 | |
RSF | 0.24886 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
10 | TSF | 0.40088 | 0.42330 | -22.61759 | 23.55569 | 0.06190 | 0.19346 |
KSF | 0.20000 | 0.42330 | -0.73281 | 1.72878 | 0.00403 | 0.19346 | |
RSF | 0.16529 | 0.40512 | -2.51889 | 3.51014 | 0.00875 | 0.24011 | |
11 | TSF | 0.42240 | 0.42768 | -160.68449 | 161.25747 | 0.42702 | 0.18229 |
KSF | 0.10000 | 0.42768 | -0.58263 | 1.57900 | 0.00363 | 0.18229 |
Covariance | 1B0012 | 1B0013 | 1B0010 | 1B0011 | 1B0006 | Returns |
1B0012 | 8.62E-05 | 1.07E-04 | -4.22E-05 | -5.38E-05 | -5.25E-05 | 0.00246 |
1B0013 | 1.07E-04 | 1.72E-04 | -1.62E-04 | -1.61E-04 | -5.79E-05 | 0.00351 |
1B0010 | -4.22E-05 | -1.62E-04 | 0.00863 | 0.00657 | 0.00830 | 0.00497 |
1B0011 | -5.38E-05 | -1.61E-04 | 0.00657 | 0.00609 | 0.00648 | 0.01214 |
1B0006 | -5.25E-05 | -5.79E-05 | 0.00830 | 0.00648 | 0.01390 | 0.00613 |
Covariance | 1B0012 | 1B0013 | 1B0010 | 1B0011 | 1B0006 | Returns |
1B0012 | 8.62E-05 | 1.07E-04 | -4.22E-05 | -5.38E-05 | -5.25E-05 | 0.00246 |
1B0013 | 1.07E-04 | 1.72E-04 | -1.62E-04 | -1.61E-04 | -5.79E-05 | 0.00351 |
1B0010 | -4.22E-05 | -1.62E-04 | 0.00863 | 0.00657 | 0.00830 | 0.00497 |
1B0011 | -5.38E-05 | -1.61E-04 | 0.00657 | 0.00609 | 0.00648 | 0.01214 |
1B0006 | -5.25E-05 | -5.79E-05 | 0.00830 | 0.00648 | 0.01390 | 0.00613 |
weight | |||||||
0.10000 | 0.20000 | 0.30000 | 0.35000 | 0.36000 | 0.37000 | 0.37984 | |
1.21251 | 1.07523 | 0.76327 | 0.20470 | -0.11043 | -0.81445 | -93.92237 | |
-0.24424 | -0.11734 | 0.17103 | 0.68736 | 0.97865 | 1.62943 | 87.69587 | |
-0.05544 | -0.07397 | -0.11610 | -0.19151 | -0.23406 | -0.32912 | -12.90054 | |
0.08093 | 0.11220 | 0.18327 | 0.31053 | 0.38232 | 0.54272 | 21.75489 | |
0.00624 | 0.00388 | -0.00148 | -0.01107 | -0.01648 | -0.02858 | -1.62785 | |
-0.21947 | -0.16942 | -0.06622 | 0.05969 | 0.10400 | 0.16515 | 0.30287 |
weight | |||||||
0.10000 | 0.20000 | 0.30000 | 0.35000 | 0.36000 | 0.37000 | 0.37984 | |
1.21251 | 1.07523 | 0.76327 | 0.20470 | -0.11043 | -0.81445 | -93.92237 | |
-0.24424 | -0.11734 | 0.17103 | 0.68736 | 0.97865 | 1.62943 | 87.69587 | |
-0.05544 | -0.07397 | -0.11610 | -0.19151 | -0.23406 | -0.32912 | -12.90054 | |
0.08093 | 0.11220 | 0.18327 | 0.31053 | 0.38232 | 0.54272 | 21.75489 | |
0.00624 | 0.00388 | -0.00148 | -0.01107 | -0.01648 | -0.02858 | -1.62785 | |
-0.21947 | -0.16942 | -0.06622 | 0.05969 | 0.10400 | 0.16515 | 0.30287 |
[1] |
Haixiang Yao, Ping Chen, Miao Zhang, Xun Li. Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation risk. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020166 |
[2] |
Bing Liu, Ming Zhou. Robust portfolio selection for individuals: Minimizing the probability of lifetime ruin. Journal of Industrial & Management Optimization, 2021, 17 (2) : 937-952. doi: 10.3934/jimo.2020005 |
[3] |
Junkee Jeon. Finite horizon portfolio selection problems with stochastic borrowing constraints. Journal of Industrial & Management Optimization, 2021, 17 (2) : 733-763. doi: 10.3934/jimo.2019132 |
[4] |
Lin Jiang, Song Wang. Robust multi-period and multi-objective portfolio selection. Journal of Industrial & Management Optimization, 2021, 17 (2) : 695-709. doi: 10.3934/jimo.2019130 |
[5] |
Nan Zhang, Linyi Qian, Zhuo Jin, Wei Wang. Optimal stop-loss reinsurance with joint utility constraints. Journal of Industrial & Management Optimization, 2021, 17 (2) : 841-868. doi: 10.3934/jimo.2020001 |
[6] |
Jiannan Zhang, Ping Chen, Zhuo Jin, Shuanming Li. Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model. Journal of Industrial & Management Optimization, 2021, 17 (2) : 765-777. doi: 10.3934/jimo.2019133 |
[7] |
Yen-Luan Chen, Chin-Chih Chang, Zhe George Zhang, Xiaofeng Chen. Optimal preventive "maintenance-first or -last" policies with generalized imperfect maintenance models. Journal of Industrial & Management Optimization, 2021, 17 (1) : 501-516. doi: 10.3934/jimo.2020149 |
[8] |
Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020347 |
[9] |
Yu Zhou, Xinfeng Dong, Yongzhuang Wei, Fengrong Zhang. A note on the Signal-to-noise ratio of $ (n, m) $-functions. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020117 |
[10] |
Manil T. Mohan. First order necessary conditions of optimality for the two dimensional tidal dynamics system. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020045 |
[11] |
Wenyan Zhuo, Honglin Yang, Leopoldo Eduardo Cárdenas-Barrón, Hong Wan. Loss-averse supply chain decisions with a capital constrained retailer. Journal of Industrial & Management Optimization, 2021, 17 (2) : 711-732. doi: 10.3934/jimo.2019131 |
[12] |
Sebastian J. Schreiber. The $ P^* $ rule in the stochastic Holt-Lawton model of apparent competition. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 633-644. doi: 10.3934/dcdsb.2020374 |
[13] |
Kohei Nakamura. An application of interpolation inequalities between the deviation of curvature and the isoperimetric ratio to the length-preserving flow. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1093-1102. doi: 10.3934/dcdss.2020385 |
[14] |
Ripeng Huang, Shaojian Qu, Xiaoguang Yang, Zhimin Liu. Multi-stage distributionally robust optimization with risk aversion. Journal of Industrial & Management Optimization, 2021, 17 (1) : 233-259. doi: 10.3934/jimo.2019109 |
[15] |
Haodong Yu, Jie Sun. Robust stochastic optimization with convex risk measures: A discretized subgradient scheme. Journal of Industrial & Management Optimization, 2021, 17 (1) : 81-99. doi: 10.3934/jimo.2019100 |
[16] |
Hongguang Ma, Xiang Li. Multi-period hazardous waste collection planning with consideration of risk stability. Journal of Industrial & Management Optimization, 2021, 17 (1) : 393-408. doi: 10.3934/jimo.2019117 |
[17] |
Jia Cai, Guanglong Xu, Zhensheng Hu. Sketch-based image retrieval via CAT loss with elastic net regularization. Mathematical Foundations of Computing, 2020, 3 (4) : 219-227. doi: 10.3934/mfc.2020013 |
[18] |
Yuyuan Ouyang, Trevor Squires. Some worst-case datasets of deterministic first-order methods for solving binary logistic regression. Inverse Problems & Imaging, 2021, 15 (1) : 63-77. doi: 10.3934/ipi.2020047 |
[19] |
Wenyuan Wang, Ran Xu. General drawdown based dividend control with fixed transaction costs for spectrally negative Lévy risk processes. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020179 |
[20] |
José Madrid, João P. G. Ramos. On optimal autocorrelation inequalities on the real line. Communications on Pure & Applied Analysis, 2021, 20 (1) : 369-388. doi: 10.3934/cpaa.2020271 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]