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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 84, 2012 - Issue 5-6: The Mark H.A. Davis festschrift: stochastics, control and finance
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Original Articles

A mean-field stochastic maximum principle via Malliavin calculus

Thilo Meyer-Brandis Center of Mathematics for Applications (CMA), University of Oslo, Box 1053 Blindern, N-0316, Oslo, Norway
,
Bernt Øksendal Center of Mathematics for Applications (CMA), University of Oslo, Box 1053 Blindern, N-0316, Oslo, Norway; Norwegian School of Economics and Business Administration (NHH), Helleveien 30, N-5045, Bergen, Norway
&
Xun Yu Zhou Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB, UK; Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong KongCorrespondence[email protected]
Pages 643-666 | Received 25 May 2010, Accepted 17 Dec 2011, Published online: 10 Feb 2012

References

  • Anderson , D. and Djehiche , B. 2011 . A maximum principle for SDE's of mean-field type . Appl. Math. Optim. , 58 : 76 – 82 .
  • Baras , J.S. , Elliott , R.J. and Kohlmann , M. 1989 . The partially observed stochastic minimum principle . SIAM J. Control Optim. , 27 : 1279 – 1292 .
  • Bensoussan , A. 1992 . Stochastic Control of Partially Observable Systems , Cambridge : Cambridge University Press .
  • Benth , F.E. , Di Nunno , G. , Løkka , A. , Øksendal , B. and Proske , F. 2003 . Explicit representation of the minimal variance portfolio in markets driven by Lévy processes . Math. Finance. , 13 : 55 – 72 .
  • Baghery , F. and Øksendal , B. 2007 . A maximum principle for stochastic control with partial information . Stoch. Anal. Appl. , 25 : 705 – 717 .
  • Di Nunno , G. , Meyer-Brandis , T. , Øksendal , B. and Proske , F. 2005 . Malliavin Calculus and anticipative Itô formulae for Lévy processes . Inf. dim. Anal. Quant. Probab. , 8 : 235 – 258 .
  • Di Nunno , G. , Øksendal , B. and Proske , F. 2009 . Malliavin Calculus for Lévy Processes and Applications to Finance , Berlin, Heidelberg : Universitext, Springer .
  • Elliott , R.J. and Kohlmann , M. 1994 . The second order minimum principle and adjoint process . Stoch. Stoch. Rep. , 46 : 25 – 39 .
  • Fourni , E. , Lasry , J.-M. , Lebuchoux , J. and Lions , P.-L. 2001 . Applications of Malliavin calculus to Monte-Carlo methods in finance. II . Finance Stoch. , 5 : 201 – 236 .
  • Itô , Y. 1988 . Generalized poisson functionals . Prob. Theory Rel. Fields , 77 : 1 – 28 .
  • B. Jourdain, S. Meleard, and W.A. Woyczynski, Nonlinear SDEs driven by Levy processes and related PDEs, Working paper, 2008
  • Karatzas , I. and Ocone , D. 1991 . A generalized Clark representation formula, with application to optimal portfolios . Stoch. Stoch. Rep. , 34 : 187 – 220 .
  • Karatzas , I. and Xue , X. 1991 . A note on utility maximization under partial observations . Math. Finance. , 1 : 57 – 70 .
  • Lakner , P. 1998 . Optimal trading strategy for an inverstor: The case of partial information . Stoch. Process. Appl. , 76 : 77 – 97 .
  • Lasry , J.-M. and Lions , P.-L. 2007 . Mean field games . Jpn J. Math , 2 : 229 – 260 .
  • Nualart , D. 2006 . Malliavin Calculus and Related Topics , 2nd ed. , Berlin, Heidelberg : Springer .
  • Øksendal , B. and Sulem , A. 2007 . Applied Stochastic Control of Jump Diffusions , 2nd ed. , Berlin, Heidelberg : Springer .
  • Øksendal , B. and Sulem , A. 2009 . Maximum principles for optimal control of forward-backward stochastic differential equations with jumps . SIAM J. Control Optim. , 48 : 2945 – 2976 .
  • Pham , H. and Quenez , M.-C. 2001 . Optimal portfolio in partially observed stochastic volatility models . Ann. Appl. Probab. , 11 : 210 – 238 .
  • Tang , S. 1998 . The Maximum principle for partially observed optimal control of stochastic differential equations . SIAM J. Control Optim. , 36 : 1596 – 1617 .
  • Yong , J. and Zhou , X.Y. 1999 . Stochastic Controls: Hamiltonian Systems and HJB Equations , New York : Springer .

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