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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), 331-345. |
[2] |
M. J. Brennan, The role of learning in dynamic portfolio decisions, European Finance Review, 1 (1998), 295-306.
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), 1050-1066.
doi: 10.1137/S036301299834185X. |
[4] |
J. Cvitanić and I. Karatzas, On dynamic measures of risk, Finance and Stochastics, 3 (1999), 451-482. |
[5] |
N. Dokuchaev, Maximin investment problems for discounted and total wealth, IMA Journal Management Mathematics, 19 (2008), 63-74.
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 non-predictable parameters: Solution via heat equation, IMA J. Management Mathematics, 17 (2006), 257-276.
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), 1239-1258.
doi: 10.1137/S036301290342557X. |
[9] |
N. G. Dokuchaev and U. Haussmann, Optimal portfolio selection and compression in an incomplete market, Quantitative Finance, 1 (2001), 336-345.
doi: 10.1088/1469-7688/1/3/305. |
[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), 385-404. |
[12] |
I. Karatzas and S. E. Shreve, "Methods of Mathematical Finance," Applications of Mathematics (New York), 39, Springer-Verlag, New York, 1998. |
[13] |
A. Khanna and M. Kulldorff, A generalization of the mutual fund theorem, Finance and Stochastics, 3 (1999), 167-185.
doi: 10.1007/s007800050056. |
[14] |
S. Komuro and H. Konno, Empirical studies on internationally diversified investment using a stock-bond integrated model, Journal of Industrial and Management Optimization, 1 (2005), 433-442. |
[15] |
D. Lambertone and B. Lapeyre, "Introduction to Stochastic Calculus Applied to Finance," Chapman & Hall, London, 1996. |
[16] |
Libin Mou and Jiongmin Yong, Two-person zero-sum linear quadratic stochastic differential games by a Hilbert space method, Journal of Industrial and Management Optimization, 2 (2006), 95-117. |
[17] |
M. Rutkowski, Self-financing trading strategies for sliding, rolling-horizon, and consol bonds, Mathematical Finance, 9 (1999), 361-385.
doi: 10.1111/1467-9965.00074. |
[18] |
W. Schachermayer, M. Sîrbu and E. Taflin, In which financial markets do mutual fund theorems hold true?, Finance and Stochastics, 13 (2009), 49-77.
doi: 10.1007/s00780-008-0072-x. |
[19] |
M. Yaari, The dual theory of choice under risk, Econometrica, 55 (1987), 95-115.
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), 331-345. |
[2] |
M. J. Brennan, The role of learning in dynamic portfolio decisions, European Finance Review, 1 (1998), 295-306.
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), 1050-1066.
doi: 10.1137/S036301299834185X. |
[4] |
J. Cvitanić and I. Karatzas, On dynamic measures of risk, Finance and Stochastics, 3 (1999), 451-482. |
[5] |
N. Dokuchaev, Maximin investment problems for discounted and total wealth, IMA Journal Management Mathematics, 19 (2008), 63-74.
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 non-predictable parameters: Solution via heat equation, IMA J. Management Mathematics, 17 (2006), 257-276.
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), 1239-1258.
doi: 10.1137/S036301290342557X. |
[9] |
N. G. Dokuchaev and U. Haussmann, Optimal portfolio selection and compression in an incomplete market, Quantitative Finance, 1 (2001), 336-345.
doi: 10.1088/1469-7688/1/3/305. |
[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), 385-404. |
[12] |
I. Karatzas and S. E. Shreve, "Methods of Mathematical Finance," Applications of Mathematics (New York), 39, Springer-Verlag, New York, 1998. |
[13] |
A. Khanna and M. Kulldorff, A generalization of the mutual fund theorem, Finance and Stochastics, 3 (1999), 167-185.
doi: 10.1007/s007800050056. |
[14] |
S. Komuro and H. Konno, Empirical studies on internationally diversified investment using a stock-bond integrated model, Journal of Industrial and Management Optimization, 1 (2005), 433-442. |
[15] |
D. Lambertone and B. Lapeyre, "Introduction to Stochastic Calculus Applied to Finance," Chapman & Hall, London, 1996. |
[16] |
Libin Mou and Jiongmin Yong, Two-person zero-sum linear quadratic stochastic differential games by a Hilbert space method, Journal of Industrial and Management Optimization, 2 (2006), 95-117. |
[17] |
M. Rutkowski, Self-financing trading strategies for sliding, rolling-horizon, and consol bonds, Mathematical Finance, 9 (1999), 361-385.
doi: 10.1111/1467-9965.00074. |
[18] |
W. Schachermayer, M. Sîrbu and E. Taflin, In which financial markets do mutual fund theorems hold true?, Finance and Stochastics, 13 (2009), 49-77.
doi: 10.1007/s00780-008-0072-x. |
[19] |
M. Yaari, The dual theory of choice under risk, Econometrica, 55 (1987), 95-115.
doi: 10.2307/1911158. |
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