
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, (eds. C. Casacuberta, et al.) (Barcelona, 2000), Progr. Math., 202, Birkhäuser, Basel, (2001), 331345. 
[2] 
M. J. Brennan, The role of learning in dynamic portfolio decisions, European Finance Review, 1 (1998), 295306. doi: 10.1023/A:1009725805128. 
[3] 
J. Cvitanić, Minimizing expected loss of hedging in incomplete and constrained markets, SIAM J. of Control and Optimization, 38 (2000), 10501066. doi: 10.1137/S036301299834185X. 
[4] 
J. Cvitanić and I. Karatzas, On dynamic measures of risk, Finance and Stochastics, 3 (1999), 451482. 
[5] 
N. Dokuchaev, Maximin investment problems for discounted and total wealth, IMA Journal Management Mathematics, 19 (2008), 6374. doi: 10.1093/imaman/dpm031. 
[6] 
N. Dokuchaev, "Mathematical Finance: Core Theory, Problems, and Statistical Algorithms," Routledge, (2007), 209 pp. doi: 10.4324/9780203964729. 
[7] 
N. Dokuchaev, Saddle points for maximin investment problems with observable but nonpredictable parameters: Solution via heat equation, IMA J. Management Mathematics, 17 (2006), 257276. doi: 10.1093/imaman/dpi041. 
[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), 12391258. doi: 10.1137/S036301290342557X. 
[9] 
N. G. Dokuchaev and U. Haussmann, Optimal portfolio selection and compression in an incomplete market, Quantitative Finance, 1 (2001), 336345. doi: 10.1088/14697688/1/3/305. 
[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, Hong Kong Polytechnic University, Working Paper, 1998. 
[11] 
N. G. Dokuchaev and K. L. Teo, Optimal hedging strategy for a portfolio investment problem with additional constraints, Dynamics of Continuous, Discrete and Impulsive Systems, 7 (2000), 385404. 
[12] 
I. Karatzas and S. E. Shreve, "Methods of Mathematical Finance," Applications of Mathematics (New York), 39, SpringerVerlag, New York, 1998. 
[13] 
A. Khanna and M. Kulldorff, A generalization of the mutual fund theorem, Finance and Stochastics, 3 (1999), 167185. doi: 10.1007/s007800050056. 
[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), 433442. 
[15] 
D. Lambertone and B. Lapeyre, "Introduction to Stochastic Calculus Applied to Finance," Chapman & Hall, London, 1996. 
[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), 95117. 
[17] 
M. Rutkowski, Selffinancing trading strategies for sliding, rollinghorizon, and consol bonds, Mathematical Finance, 9 (1999), 361385. doi: 10.1111/14679965.00074. 
[18] 
W. Schachermayer, M. Sîrbu and E. Taflin, In which financial markets do mutual fund theorems hold true?, Finance and Stochastics, 13 (2009), 4977. doi: 10.1007/s007800080072x. 
[19] 
M. Yaari, The dual theory of choice under risk, Econometrica, 55 (1987), 95115. doi: 10.2307/1911158. 
show all references
References:
[1] 
T. R. Bielecki and S. R. Pliska, Risk sensitive control with applications to fixed income portfolio management, (eds. C. Casacuberta, et al.) (Barcelona, 2000), Progr. Math., 202, Birkhäuser, Basel, (2001), 331345. 
[2] 
M. J. Brennan, The role of learning in dynamic portfolio decisions, European Finance Review, 1 (1998), 295306. doi: 10.1023/A:1009725805128. 
[3] 
J. Cvitanić, Minimizing expected loss of hedging in incomplete and constrained markets, SIAM J. of Control and Optimization, 38 (2000), 10501066. doi: 10.1137/S036301299834185X. 
[4] 
J. Cvitanić and I. Karatzas, On dynamic measures of risk, Finance and Stochastics, 3 (1999), 451482. 
[5] 
N. Dokuchaev, Maximin investment problems for discounted and total wealth, IMA Journal Management Mathematics, 19 (2008), 6374. doi: 10.1093/imaman/dpm031. 
[6] 
N. Dokuchaev, "Mathematical Finance: Core Theory, Problems, and Statistical Algorithms," Routledge, (2007), 209 pp. doi: 10.4324/9780203964729. 
[7] 
N. Dokuchaev, Saddle points for maximin investment problems with observable but nonpredictable parameters: Solution via heat equation, IMA J. Management Mathematics, 17 (2006), 257276. doi: 10.1093/imaman/dpi041. 
[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), 12391258. doi: 10.1137/S036301290342557X. 
[9] 
N. G. Dokuchaev and U. Haussmann, Optimal portfolio selection and compression in an incomplete market, Quantitative Finance, 1 (2001), 336345. doi: 10.1088/14697688/1/3/305. 
[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, Hong Kong Polytechnic University, Working Paper, 1998. 
[11] 
N. G. Dokuchaev and K. L. Teo, Optimal hedging strategy for a portfolio investment problem with additional constraints, Dynamics of Continuous, Discrete and Impulsive Systems, 7 (2000), 385404. 
[12] 
I. Karatzas and S. E. Shreve, "Methods of Mathematical Finance," Applications of Mathematics (New York), 39, SpringerVerlag, New York, 1998. 
[13] 
A. Khanna and M. Kulldorff, A generalization of the mutual fund theorem, Finance and Stochastics, 3 (1999), 167185. doi: 10.1007/s007800050056. 
[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), 433442. 
[15] 
D. Lambertone and B. Lapeyre, "Introduction to Stochastic Calculus Applied to Finance," Chapman & Hall, London, 1996. 
[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), 95117. 
[17] 
M. Rutkowski, Selffinancing trading strategies for sliding, rollinghorizon, and consol bonds, Mathematical Finance, 9 (1999), 361385. doi: 10.1111/14679965.00074. 
[18] 
W. Schachermayer, M. Sîrbu and E. Taflin, In which financial markets do mutual fund theorems hold true?, Finance and Stochastics, 13 (2009), 4977. doi: 10.1007/s007800080072x. 
[19] 
M. Yaari, The dual theory of choice under risk, Econometrica, 55 (1987), 95115. doi: 10.2307/1911158. 
[1] 
Zheng Dou, Shaoyong Lai. Optimal contracts and asset prices in a continuoustime delegated portfolio management problem. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022083 
[2] 
Aleksandar Jović. Saddlepoint type optimality criteria, duality and a new approach for solving nonsmooth fractional continuoustime programming problems. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022025 
[3] 
Zhihong Xia, Peizheng Yu. A fixed point theorem for twist maps. Discrete and Continuous Dynamical Systems, 2022, 42 (8) : 40514059. doi: 10.3934/dcds.2022045 
[4] 
Zhengyan Wang, Guanghua Xu, Peibiao Zhao, Zudi Lu. The optimal cash holding models for stochastic cash management of continuous time. Journal of Industrial and Management Optimization, 2018, 14 (1) : 117. doi: 10.3934/jimo.2017034 
[5] 
Hui Meng, Fei Lung Yuen, Tak Kuen Siu, Hailiang Yang. Optimal portfolio in a continuoustime selfexciting threshold model. Journal of Industrial and Management Optimization, 2013, 9 (2) : 487504. doi: 10.3934/jimo.2013.9.487 
[6] 
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 
[7] 
Luis HernándezCorbato, Francisco R. Ruiz del Portal. Fixed point indices of planar continuous maps. Discrete and Continuous Dynamical Systems, 2015, 35 (7) : 29792995. doi: 10.3934/dcds.2015.35.2979 
[8] 
Ovide Arino, Eva Sánchez. A saddle point theorem for functional statedependent delay differential equations. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 687722. doi: 10.3934/dcds.2005.12.687 
[9] 
Hanqing Jin, Xun Yu Zhou. Continuoustime portfolio selection under ambiguity. Mathematical Control and Related Fields, 2015, 5 (3) : 475488. doi: 10.3934/mcrf.2015.5.475 
[10] 
Gastão S. F. Frederico, Delfim F. M. Torres. Noether's symmetry Theorem for variational and optimal control problems with time delay. Numerical Algebra, Control and Optimization, 2012, 2 (3) : 619630. doi: 10.3934/naco.2012.2.619 
[11] 
Zaidong Zhan, Shuping Chen, Wei Wei. A unified theory of maximum principle for continuous and discrete time optimal control problems. Mathematical Control and Related Fields, 2012, 2 (2) : 195215. doi: 10.3934/mcrf.2012.2.195 
[12] 
XiaoFei Peng, Wen Li. A new BramblePasciaklike preconditioner for saddle point problems. Numerical Algebra, Control and Optimization, 2012, 2 (4) : 823838. doi: 10.3934/naco.2012.2.823 
[13] 
Mircea Sofonea, Cezar Avramescu, Andaluzia Matei. A fixed point result with applications in the study of viscoplastic frictionless contact problems. Communications on Pure and Applied Analysis, 2008, 7 (3) : 645658. doi: 10.3934/cpaa.2008.7.645 
[14] 
Chenchen Zu, Xiaoqi Yang, Carisa Kwok Wai Yu. Sparse minimax portfolio and Sharpe ratio models. Journal of Industrial and Management Optimization, 2022, 18 (5) : 32473262. doi: 10.3934/jimo.2021111 
[15] 
Chao Deng, Haixiang Yao, Yan Chen. Optimal investment and risk control problems with delay for an insurer in defaultable market. Journal of Industrial and Management Optimization, 2020, 16 (5) : 25632579. doi: 10.3934/jimo.2019070 
[16] 
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 
[17] 
Lars Grüne, Roberto Guglielmi. On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems. Mathematical Control and Related Fields, 2021, 11 (1) : 169188. doi: 10.3934/mcrf.2020032 
[18] 
JoseLuis RocaGonzalez. Designing dynamical systems for security and defence network knowledge management. A case of study: Airport bird control falconers organizations. Discrete and Continuous Dynamical Systems  S, 2015, 8 (6) : 13111329. doi: 10.3934/dcdss.2015.8.1311 
[19] 
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 
[20] 
Yan Zeng, Zhongfei Li, Jingjun Liu. Optimal strategies of benchmark and meanvariance portfolio selection problems for insurers. Journal of Industrial and Management Optimization, 2010, 6 (3) : 483496. doi: 10.3934/jimo.2010.6.483 
2021 Impact Factor: 1.497
Tools
Metrics
Other articles
by authors
[Back to Top]