
Previous Article
Feature extraction of the patterned textile with deformations via optimal control theory
 DCDSB Home
 This Issue

Next Article
Preface
Dimension reduction and Mutual Fund Theorem in maximin setting for bond market
1.  Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, Western Australia, 6845, Australia 
References:
[1] 
T. R. Bielecki and S. R. Pliska, Risk sensitive control with applications to fixed income portfolio management,, "European Congress of Mathematics, Vol. II", 202 (2001), 331. Google Scholar 
[2] 
M. J. Brennan, The role of learning in dynamic portfolio decisions,, European Finance Review, 1 (1998), 295. doi: 10.1023/A:1009725805128. Google Scholar 
[3] 
J. Cvitanić, Minimizing expected loss of hedging in incomplete and constrained markets,, SIAM J. of Control and Optimization, 38 (2000), 1050. doi: 10.1137/S036301299834185X. Google Scholar 
[4] 
J. Cvitanić and I. Karatzas, On dynamic measures of risk,, Finance and Stochastics, 3 (1999), 451. Google Scholar 
[5] 
N. Dokuchaev, Maximin investment problems for discounted and total wealth,, IMA Journal Management Mathematics, 19 (2008), 63. doi: 10.1093/imaman/dpm031. Google Scholar 
[6] 
N. Dokuchaev, "Mathematical Finance: Core Theory, Problems, and Statistical Algorithms,", Routledge, (2007). doi: 10.4324/9780203964729. Google Scholar 
[7] 
N. Dokuchaev, Saddle points for maximin investment problems with observable but nonpredictable parameters: Solution via heat equation,, IMA J. Management Mathematics, 17 (2006), 257. doi: 10.1093/imaman/dpi041. Google Scholar 
[8] 
N. G. Dokuchaev, Optimal solution of investment problems via linear parabolic equations generated by Kalman filter,, SIAM J. of Control and Optimization, 44 (2005), 1239. doi: 10.1137/S036301290342557X. Google Scholar 
[9] 
N. G. Dokuchaev and U. Haussmann, Optimal portfolio selection and compression in an incomplete market,, Quantitative Finance, 1 (2001), 336. doi: 10.1088/14697688/1/3/305. Google Scholar 
[10] 
N. G. Dokuchaev and K. L. Teo, "A Duality Approach to an Optimal Investment Problem with Unknown and Nonobservable Parameters,", Department of Applied Mathematics, (1998). Google Scholar 
[11] 
N. G. Dokuchaev and K. L. Teo, Optimal hedging strategy for a portfolio investment problem with additional constraints,, Dynamics of Continuous, 7 (2000), 385. Google Scholar 
[12] 
I. Karatzas and S. E. Shreve, "Methods of Mathematical Finance,", Applications of Mathematics (New York), 39 (1998). Google Scholar 
[13] 
A. Khanna and M. Kulldorff, A generalization of the mutual fund theorem,, Finance and Stochastics, 3 (1999), 167. doi: 10.1007/s007800050056. Google Scholar 
[14] 
S. Komuro and H. Konno, Empirical studies on internationally diversified investment using a stockbond integrated model,, Journal of Industrial and Management Optimization, 1 (2005), 433. Google Scholar 
[15] 
D. Lambertone and B. Lapeyre, "Introduction to Stochastic Calculus Applied to Finance,", Chapman & Hall, (1996). Google Scholar 
[16] 
Libin Mou and Jiongmin Yong, Twoperson zerosum linear quadratic stochastic differential games by a Hilbert space method,, Journal of Industrial and Management Optimization, 2 (2006), 95. Google Scholar 
[17] 
M. Rutkowski, Selffinancing trading strategies for sliding, rollinghorizon, and consol bonds,, Mathematical Finance, 9 (1999), 361. doi: 10.1111/14679965.00074. Google Scholar 
[18] 
W. Schachermayer, M. Sîrbu and E. Taflin, In which financial markets do mutual fund theorems hold true?,, Finance and Stochastics, 13 (2009), 49. doi: 10.1007/s007800080072x. Google Scholar 
[19] 
M. Yaari, The dual theory of choice under risk,, Econometrica, 55 (1987), 95. doi: 10.2307/1911158. Google Scholar 
show all references
References:
[1] 
T. R. Bielecki and S. R. Pliska, Risk sensitive control with applications to fixed income portfolio management,, "European Congress of Mathematics, Vol. II", 202 (2001), 331. Google Scholar 
[2] 
M. J. Brennan, The role of learning in dynamic portfolio decisions,, European Finance Review, 1 (1998), 295. doi: 10.1023/A:1009725805128. Google Scholar 
[3] 
J. Cvitanić, Minimizing expected loss of hedging in incomplete and constrained markets,, SIAM J. of Control and Optimization, 38 (2000), 1050. doi: 10.1137/S036301299834185X. Google Scholar 
[4] 
J. Cvitanić and I. Karatzas, On dynamic measures of risk,, Finance and Stochastics, 3 (1999), 451. Google Scholar 
[5] 
N. Dokuchaev, Maximin investment problems for discounted and total wealth,, IMA Journal Management Mathematics, 19 (2008), 63. doi: 10.1093/imaman/dpm031. Google Scholar 
[6] 
N. Dokuchaev, "Mathematical Finance: Core Theory, Problems, and Statistical Algorithms,", Routledge, (2007). doi: 10.4324/9780203964729. Google Scholar 
[7] 
N. Dokuchaev, Saddle points for maximin investment problems with observable but nonpredictable parameters: Solution via heat equation,, IMA J. Management Mathematics, 17 (2006), 257. doi: 10.1093/imaman/dpi041. Google Scholar 
[8] 
N. G. Dokuchaev, Optimal solution of investment problems via linear parabolic equations generated by Kalman filter,, SIAM J. of Control and Optimization, 44 (2005), 1239. doi: 10.1137/S036301290342557X. Google Scholar 
[9] 
N. G. Dokuchaev and U. Haussmann, Optimal portfolio selection and compression in an incomplete market,, Quantitative Finance, 1 (2001), 336. doi: 10.1088/14697688/1/3/305. Google Scholar 
[10] 
N. G. Dokuchaev and K. L. Teo, "A Duality Approach to an Optimal Investment Problem with Unknown and Nonobservable Parameters,", Department of Applied Mathematics, (1998). Google Scholar 
[11] 
N. G. Dokuchaev and K. L. Teo, Optimal hedging strategy for a portfolio investment problem with additional constraints,, Dynamics of Continuous, 7 (2000), 385. Google Scholar 
[12] 
I. Karatzas and S. E. Shreve, "Methods of Mathematical Finance,", Applications of Mathematics (New York), 39 (1998). Google Scholar 
[13] 
A. Khanna and M. Kulldorff, A generalization of the mutual fund theorem,, Finance and Stochastics, 3 (1999), 167. doi: 10.1007/s007800050056. Google Scholar 
[14] 
S. Komuro and H. Konno, Empirical studies on internationally diversified investment using a stockbond integrated model,, Journal of Industrial and Management Optimization, 1 (2005), 433. Google Scholar 
[15] 
D. Lambertone and B. Lapeyre, "Introduction to Stochastic Calculus Applied to Finance,", Chapman & Hall, (1996). Google Scholar 
[16] 
Libin Mou and Jiongmin Yong, Twoperson zerosum linear quadratic stochastic differential games by a Hilbert space method,, Journal of Industrial and Management Optimization, 2 (2006), 95. Google Scholar 
[17] 
M. Rutkowski, Selffinancing trading strategies for sliding, rollinghorizon, and consol bonds,, Mathematical Finance, 9 (1999), 361. doi: 10.1111/14679965.00074. Google Scholar 
[18] 
W. Schachermayer, M. Sîrbu and E. Taflin, In which financial markets do mutual fund theorems hold true?,, Finance and Stochastics, 13 (2009), 49. doi: 10.1007/s007800080072x. Google Scholar 
[19] 
M. Yaari, The dual theory of choice under risk,, Econometrica, 55 (1987), 95. doi: 10.2307/1911158. Google Scholar 
[1] 
Zhengyan Wang, Guanghua Xu, Peibiao Zhao, Zudi Lu. The optimal cash holding models for stochastic cash management of continuous time. Journal of Industrial & Management Optimization, 2018, 14 (1) : 117. doi: 10.3934/jimo.2017034 
[2] 
Hui Meng, Fei Lung Yuen, Tak Kuen Siu, Hailiang Yang. Optimal portfolio in a continuoustime selfexciting threshold model. Journal of Industrial & Management Optimization, 2013, 9 (2) : 487504. doi: 10.3934/jimo.2013.9.487 
[3] 
Luis HernándezCorbato, Francisco R. Ruiz del Portal. Fixed point indices of planar continuous maps. Discrete & Continuous Dynamical Systems  A, 2015, 35 (7) : 29792995. doi: 10.3934/dcds.2015.35.2979 
[4] 
ShuiHung Hou. On an application of fixed point theorem to nonlinear inclusions. Conference Publications, 2011, 2011 (Special) : 692697. doi: 10.3934/proc.2011.2011.692 
[5] 
Ovide Arino, Eva Sánchez. A saddle point theorem for functional statedependent delay differential equations. Discrete & Continuous Dynamical Systems  A, 2005, 12 (4) : 687722. doi: 10.3934/dcds.2005.12.687 
[6] 
Hanqing Jin, Xun Yu Zhou. Continuoustime portfolio selection under ambiguity. Mathematical Control & Related Fields, 2015, 5 (3) : 475488. doi: 10.3934/mcrf.2015.5.475 
[7] 
Zaidong Zhan, Shuping Chen, Wei Wei. A unified theory of maximum principle for continuous and discrete time optimal control problems. Mathematical Control & Related Fields, 2012, 2 (2) : 195215. doi: 10.3934/mcrf.2012.2.195 
[8] 
Gastão S. F. Frederico, Delfim F. M. Torres. Noether's symmetry Theorem for variational and optimal control problems with time delay. Numerical Algebra, Control & Optimization, 2012, 2 (3) : 619630. doi: 10.3934/naco.2012.2.619 
[9] 
XiaoFei Peng, Wen Li. A new BramblePasciaklike preconditioner for saddle point problems. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 823838. doi: 10.3934/naco.2012.2.823 
[10] 
Mircea Sofonea, Cezar Avramescu, Andaluzia Matei. A fixed point result with applications in the study of viscoplastic frictionless contact problems. Communications on Pure & Applied Analysis, 2008, 7 (3) : 645658. doi: 10.3934/cpaa.2008.7.645 
[11] 
Jeffrey W. Lyons. An application of an avery type fixed point theorem to a second order antiperiodic boundary value problem. Conference Publications, 2015, 2015 (special) : 775782. doi: 10.3934/proc.2015.0775 
[12] 
Chao Deng, Haixiang Yao, Yan Chen. Optimal investment and risk control problems with delay for an insurer in defaultable market. Journal of Industrial & Management Optimization, 2017, 13 (5) : 117. doi: 10.3934/jimo.2019070 
[13] 
Yan Zeng, Zhongfei Li, Jingjun Liu. Optimal strategies of benchmark and meanvariance portfolio selection problems for insurers. Journal of Industrial & Management Optimization, 2010, 6 (3) : 483496. doi: 10.3934/jimo.2010.6.483 
[14] 
JoseLuis RocaGonzalez. Designing dynamical systems for security and defence network knowledge management. A case of study: Airport bird control falconers organizations. Discrete & Continuous Dynamical Systems  S, 2015, 8 (6) : 13111329. doi: 10.3934/dcdss.2015.8.1311 
[15] 
K. Q. Lan, G. C. Yang. Optimal constants for two point boundary value problems. Conference Publications, 2007, 2007 (Special) : 624633. doi: 10.3934/proc.2007.2007.624 
[16] 
HuaiNian Zhu, ChengKe Zhang, Zhuo Jin. Continuoustime meanvariance assetliability management with stochastic interest rates and inflation risks. Journal of Industrial & Management Optimization, 2017, 13 (5) : 122. doi: 10.3934/jimo.2018180 
[17] 
Ping Chen, Haixiang Yao. Continuoustime meanvariance portfolio selection with noshorting constraints and regimeswitching. Journal of Industrial & Management Optimization, 2017, 13 (5) : 121. doi: 10.3934/jimo.2018166 
[18] 
Nicholas Long. Fixed point shifts of inert involutions. Discrete & Continuous Dynamical Systems  A, 2009, 25 (4) : 12971317. doi: 10.3934/dcds.2009.25.1297 
[19] 
Ping Liu, Junping Shi, Yuwen Wang. A double saddlenode bifurcation theorem. Communications on Pure & Applied Analysis, 2013, 12 (6) : 29232933. doi: 10.3934/cpaa.2013.12.2923 
[20] 
Anthony M. Bloch, Peter E. Crouch, Nikolaj Nordkvist. Continuous and discrete embedded optimal control problems and their application to the analysis of Clebsch optimal control problems and mechanical systems. Journal of Geometric Mechanics, 2013, 5 (1) : 138. doi: 10.3934/jgm.2013.5.1 
2018 Impact Factor: 1.008
Tools
Metrics
Other articles
by authors
[Back to Top]