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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. 
[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. 
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