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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. Google Scholar 
[2] 
M. J. Brennan, The role of learning in dynamic portfolio decisions, European Finance Review, 1 (1998), 295306. 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), 10501066. doi: 10.1137/S036301299834185X. Google Scholar 
[4] 
J. Cvitanić and I. Karatzas, On dynamic measures of risk, Finance and Stochastics, 3 (1999), 451482. Google Scholar 
[5] 
N. Dokuchaev, Maximin investment problems for discounted and total wealth, IMA Journal Management Mathematics, 19 (2008), 6374. doi: 10.1093/imaman/dpm031. Google Scholar 
[6] 
N. Dokuchaev, "Mathematical Finance: Core Theory, Problems, and Statistical Algorithms," Routledge, (2007), 209 pp. 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), 257276. 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), 12391258. 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), 336345. 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, Hong Kong Polytechnic University, Working Paper, 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, Discrete and Impulsive Systems, 7 (2000), 385404. Google Scholar 
[12] 
I. Karatzas and S. E. Shreve, "Methods of Mathematical Finance," Applications of Mathematics (New York), 39, SpringerVerlag, New York, 1998. Google Scholar 
[13] 
A. Khanna and M. Kulldorff, A generalization of the mutual fund theorem, Finance and Stochastics, 3 (1999), 167185. 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), 433442. Google Scholar 
[15] 
D. Lambertone and B. Lapeyre, "Introduction to Stochastic Calculus Applied to Finance," Chapman & Hall, London, 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), 95117. Google Scholar 
[17] 
M. Rutkowski, Selffinancing trading strategies for sliding, rollinghorizon, and consol bonds, Mathematical Finance, 9 (1999), 361385. 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), 4977. doi: 10.1007/s007800080072x. Google Scholar 
[19] 
M. Yaari, The dual theory of choice under risk, Econometrica, 55 (1987), 95115. 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, (eds. C. Casacuberta, et al.) (Barcelona, 2000), Progr. Math., 202, Birkhäuser, Basel, (2001), 331345. Google Scholar 
[2] 
M. J. Brennan, The role of learning in dynamic portfolio decisions, European Finance Review, 1 (1998), 295306. 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), 10501066. doi: 10.1137/S036301299834185X. Google Scholar 
[4] 
J. Cvitanić and I. Karatzas, On dynamic measures of risk, Finance and Stochastics, 3 (1999), 451482. Google Scholar 
[5] 
N. Dokuchaev, Maximin investment problems for discounted and total wealth, IMA Journal Management Mathematics, 19 (2008), 6374. doi: 10.1093/imaman/dpm031. Google Scholar 
[6] 
N. Dokuchaev, "Mathematical Finance: Core Theory, Problems, and Statistical Algorithms," Routledge, (2007), 209 pp. 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), 257276. 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), 12391258. 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), 336345. 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, Hong Kong Polytechnic University, Working Paper, 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, Discrete and Impulsive Systems, 7 (2000), 385404. Google Scholar 
[12] 
I. Karatzas and S. E. Shreve, "Methods of Mathematical Finance," Applications of Mathematics (New York), 39, SpringerVerlag, New York, 1998. Google Scholar 
[13] 
A. Khanna and M. Kulldorff, A generalization of the mutual fund theorem, Finance and Stochastics, 3 (1999), 167185. 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), 433442. Google Scholar 
[15] 
D. Lambertone and B. Lapeyre, "Introduction to Stochastic Calculus Applied to Finance," Chapman & Hall, London, 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), 95117. Google Scholar 
[17] 
M. Rutkowski, Selffinancing trading strategies for sliding, rollinghorizon, and consol bonds, Mathematical Finance, 9 (1999), 361385. 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), 4977. doi: 10.1007/s007800080072x. Google Scholar 
[19] 
M. Yaari, The dual theory of choice under risk, Econometrica, 55 (1987), 95115. doi: 10.2307/1911158. Google Scholar 
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