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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 82, 2010 - Issue 1: Special issue on Filtering and Stochastic Control
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Original Articles

On Bellman's equations for mean and variance control of a Markov diffusion

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Pages 41-51 | Received 04 Dec 2007, Accepted 21 Oct 2008, Published online: 16 Feb 2010

References

  • Darling , D.A. and Kac , M. 1957 . On occupation times for Markoff processes . Trans. Amer. Math. Soc. , 84 ( 2 ) : 444 – 458 .
  • Dynkin , E.B. 1965 . Introduction to Markov Processes , Vol. 2 , Berlin : Springer-Verlag .
  • Fitzsimmons , P.J. and Pitman , J. 1999 . Kac's moment formula and the Feynman–Kac formula for additive functionals of a Markov process . Stochastic Process. Appl. , 79 : 117 – 134 .
  • Föllmer , H. and Schweizer , M. 1991 . “ Hedging of contingent claims under incomplete information ” . In Applied Stochastic Analysis , Edited by: Davis , M.H.A. and Elliott , R.J. 389 – 414 . London : Gordon and Breach .
  • Föllmer , H. and Sondermann , D. 1986 . “ Hedging of non-redundant contingent claims ” . In Contributions to Mathematical Economics in Honor of Gérard Debreu , Edited by: Hildenbrand , W. and Mas-Colell , A. 205 – 223 . Amsterdam : North-Holland .
  • Gourieroux , C. , Laurent , J.P. and Pham , H. 1998 . Mean–variance hedging and numéraire . Math. Finance , 8 ( 3 ) : 179 – 200 .
  • Kac , M. 1949 . On distributions of certain Wiener functionals . Trans. Amer. Math. Soc. , 65 ( 1 ) : 1 – 13 .
  • Krylov , N.V. 1973 . On the selection of a Markov process from a system of processes and the construction of quasi-diffusion processes . Math. USSR Izestija , 7 ( 3 ) : 691 – 708 . (English translation)
  • Krylov , N.V. 1980 . Controlled Diffusion Processes , New York : Springer-Verlag .
  • Krylov , N.V. 1994 . Introduction to the Theory of Diffusion Processes , Providence, RI : AMS .
  • Ladyzhenskaya , O.A. , Solonnikov , V.A. and Uralceva , N.N. 1998 . Linear and Quasi-linear Equations of Parabolic Type , Providence, RI : AMS .
  • Laurent , J.P. and Pham , H. 1999 . Dynamic programming and mean–variance hedging . Finance Stoch. , 3 : 83 – 110 .
  • Markowitz , H.M. 1952 . Portfolio selection . J. Finance , 7 ( 1 ) : 77 – 91 .
  • Schweizer , M. 1992 . Mean–variance hedging for general claims . Ann. Appl. Probab. , 2 : 171 – 179 .
  • Veretennikov , A.Yu. 1982 . Parabolic equations and Ito stochastic equations with coefficients discontinuous in the time variable . Math. Notes. , 31 ( 3–4 ) : 278 – 283 .
  • Veretennikov , A.Yu. 2001 . On polynomial mixing estimates for stochastic differential equations with a gradient drift . Theory Probab. Appl. , 45 ( 1 ) : 160 – 163 .
  • Zhou , X.Y. and Li , D. 2000 . Continuous-time mean–variance portfolio selection: a stochastic LQ framework . Appl. Math. Optim. , 42 : 19 – 33 . DOI: 10.1007/s002450010003

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