Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

References

• Ait Rami , M , Chen , X and Zhou , XY . 2002 . Discrete-Time Indefinite LQ Control with State and Control Dependent Noises . Journal of Global Optimization , 23 : 245 – 265 .
   Web of Science ®Google Scholar
• Ait Rami , M and Zhou , XY . 2000 . Linear Matrix Inequalities, Riccati Equations, and Indefinite Stochastic Linear Quadratic Controls . IEEE Transactions on Automatic Control , 45 : 1131 – 1143 .
   Web of Science ®Google Scholar
• Beghi , A and D'Alessandro , D . 1998 . Discrete-Time Optimal Control with Control-Dependent Noise and Generalized Riccati Difference Equations . Automatica , 34 : 1031 – 1034 .
   Web of Science ®Google Scholar
• Boukas , EK and Liu , ZK . 2004 . Delay-Dependent Stabilisation of Singularly Perturbed Jump Linear Systems . International Journal of Control , 77 : 310 – 319 .
   Web of Science ®Google Scholar
• Cakmak , U and Ozeckici , S . 2006 . Portfolio Optimization in Stochastic Markets . Mathematical Methods of Operations Research , 63 : 151 – 168 .
   Web of Science ®Google Scholar
• Chen , S , Li , X and Zhou , XY . 1998a . Stochastic Linear Quadratic Regulators with Indefinite Control Weight Costs . SIAM Journal of Control Optimisation , 36 : 1685 – 1702 .
   Web of Science ®Google Scholar
• Chen , S , Li , X and Zhou , XY . 1998b . Stochastic Linear Quadratic Regulators with Indefinite Control Weight Costs . SIAM Journal of Control Optimisation , 36 : 1685 – 1702 .
   Web of Science ®Google Scholar
• Costa , OLV and Araujo , MV . 2008 . A Generalized Multi-Period Mean-Variance Portfolio Optimisation with Markov Switching Parameters . Automatica , 44 October 2008, to appear
   Google Scholar
• Costa , OLV and de Paulo , WL . 2007 . Indefinite Quadratic with Linear Cost Optimal Control of Markovian Jump with Multiplicative Noise Systems . Automatica , 43 : 587 – 597 .
   Web of Science ®Google Scholar
• Costa , OLV , Fragoso , MD and Marques , RP . 2005 . Discrete-Time Markov Jump Linear Systems , London : Springer-Verlag .
   Google Scholar
• Costa , OLV and Nabholz , RB . 2007 . Multiperiod Mean-Variance Optimization with Intertemporal Restrictions . Journal of Optimisation Theory and Applications , 134 : 257 – 274 .
   Web of Science ®Google Scholar
• Costa , OLV and Okimura , R . 2007 . Multi-Period Mean Variance Optimal Control of Markov Jump with Multiplicative Noise Systems . Mathematical Reports , 9 : 21 – 34 .
   Google Scholar
• Dragan , V and Morozan , T . 2006a . Mean Square Exponential Stability For Some Stochastic Linear Discrete-Time Systems . European Journal of Control , 11 : 1 – 23 .
   Google Scholar
• Dragan , V and Morozan , T . 2006b . Observability and Detectability of a class of Discrete-Time Stochastic Linear systems . IMA Journal of Mathematical Control and Information , 23 : 371 – 394 .
   Web of Science ®Google Scholar
• Dombrovskii , VV and Lyashenko , EA . 2003 . A Linear Quadratic Control For Discrete Systems with Random Parameters and Multiplicative Noise and Its Application to Investment Portfolio Optimisation . Automatic and Remote Control , 64 : 1558 – 1570 .
   Web of Science ®Google Scholar
• Elliott , RJ , Dufour , F and Malcolm , WP . 2005 . State and Mode Estimation For Discrete-Time Jump Markov Systems . SIAM Journal on Control and Optimisation , 44 : 1081 – 1104 .
   Web of Science ®Google Scholar
• Elton , EJ and Gruber , MJ . 1995 . Modern Portfolio Theory and Investment Analysis , New York : Wiley .
   Google Scholar
• Howe , MA , Rustem , B and Selby , MJP . 1996 . Multi-Period Minimax Hedging Strategies . European Journal of Operational Research , 93 : 185 – 204 .
   Google Scholar
• Howe , MA and Rustem , B . 1997 . A Robust Hedging Algorithm . Journal of Economic Dynamics and Control , 21 : 1065 – 1092 .
   Google Scholar
• Leippold , M , Trojani , F and Vanini , P . 2004 . A Geometric Approach to Multiperiod Mean Variance Optimization of Assets and Liabilities . Journal of Economic Dynamics and Control , 28 : 1079 – 1113 .
   Web of Science ®Google Scholar
• Li , D and Ng , WL . 2000 . Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation . Mathematical Finance , 10 : 387 – 406 .
   Web of Science ®Google Scholar
• Li , X , Zhou , XY and Ait Rami , M . 2003 . Indefinite Stochastic Linear Quadratic Control with Markovian Jumps in Infinite Time Horizon . Journal of Global Optimization , 27 : 149 – 175 .
   Web of Science ®Google Scholar
• Lim , A and Zhou , XY . 1999 . Stochastic Optimal Control LQR Control with Integral Quadratic Constraints and Indefinite Control weights . IEEE Transactions on Automatic Control , 44 : 1359 – 1369 .
   Web of Science ®Google Scholar
• Markowitz , H . 1959 . Portfolio Selection: Efficient Diversification of Investments , New York : John Wiley .
   Google Scholar
• Moore , JB , Zhou , XY and Lim , AEB . 1999 . Discrete-time LQG Controls with Control Dependent Noise . Systems & Control Letters , 36 : 199 – 206 .
   Web of Science ®Google Scholar
• Rustem , B , Becker , RG and Marty , W . 1995 . Robust min–max Portfolio Strategies For Rival Forecast and Risk Scenarios . Journal of Economic Dynamics and Control , 24 : 1591 – 1621 .
   Google Scholar
• Saberi , A , Sannuti , P and Chen , BM . 1995 . H ₂-Optimal Control , Upper Saddle River, NJ : Prentice Hall .
   Google Scholar
• Steinbach , MC . 2001 . Markowitz Revisited: Mean-Variance Models in Financial Portfolio Analysis . SIAM Review , 43 : 31 – 85 .
   Web of Science ®Google Scholar
• Wu , H and Zhou , XY . 2002 . Characterizing All Optimal Controls For an Indefinite Stochastic Linear Quadratic Control Problem . IEEE Transactions on Automatic Control , 47 : 1119 – 1122 .
   Web of Science ®Google Scholar
• Yin , G and Zhou , XY . 2004 . Markowitz's Mean-Variance Portfolio Selection with Regime Switching: From Discrete-Time Models to Their Continuous-Time Limits . IEEE Transactions on Automatic Control , 49 : 349 – 360 .
   Web of Science ®Google Scholar
• Zhou , XY and Li , D . 2000 . Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework . Applied Mathematics and Optimisation , 42 : 19 – 33 .
   Web of Science ®Google Scholar
• Zhou , XY and Yin , G . 2003 . Markowitz's Mean-Variance Portfolio Selection with Regime Switching: A Continuous-Time Model . SIAM Journal of Control and Optimisation , 42 : 1466 – 1482 .
   Web of Science ®Google Scholar
• Zhu , J . 2005 . on Stochastic Riccati Equations For The Stochastic LQR Problem . Systems & Control Letters , 54 : 119 – 124 .
   Google Scholar
• Zhu , SS , Li , D and Wang , SY . 2004 . Risk control Over Bankruptcy Dynamic Portfolio Selection: A Generalised Mean Variance Formulation . IEEE Transactions on Automatic Control , 49 : 447 – 457 .
   Web of Science ®Google Scholar