Table of Contents
International Journal of Stochastic Analysis
Volume 2014, Article ID 159519, 16 pages
http://dx.doi.org/10.1155/2014/159519
Research Article

A Two-Mode Mean-Field Optimal Switching Problem for the Full Balance Sheet

Department of Mathematics, KTH-Royal Institute of Technology, 100 44 Stockholm, Sweden

Received 20 February 2014; Accepted 4 May 2014; Published 25 May 2014

Academic Editor: Qing Zhang

Copyright © 2014 Boualem Djehiche and Ali Hamdi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. Djehiche and A. A. Hamdi, “Full balance sheet two-modes optimal switching problem,” Preprint, 2011.
  2. N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng, and M. C. Quenez, “Reflected solutions of backward SDE's, and related obstacle problems for PDE's,” The Annals of Probability, vol. 25, no. 2, pp. 702–737, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  3. V. S. Borkar and K. S. Kumar, “McKean-Vlasov limit in portfolio optimization,” Stochastic Analysis and Applications, vol. 28, no. 5, pp. 884–906, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  4. J. M. Lasry and P. L. Lions, “Mean field games,” Japanese Journal of Mathematics, vol. 2, no. 1, pp. 229–260, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  5. R. Buckdahn, B. Djehiche, J. Li, and S. Peng, “Mean-field backward stochastic differential equations: a limit approach,” The Annals of Probability, vol. 37, no. 4, pp. 1524–1565, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  6. R. Buckdahn, J. Li, and S. Peng, “Mean-field backward stochastic differential equations and related partial differential equations,” Stochastic Processes and Their Applications, vol. 119, no. 10, pp. 3133–3154, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  7. J. Li, “Reflected mean-field backward stochastic differential equations. Approximation and associated nonlinear PDEs,” Journal of Mathematical Analysis and Applications, vol. 413, no. 1, pp. 47–68, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  8. Z. Li and J. Luo, “Mean-field reflected backward stochastic differential equations,” Statistics & Probability Letters, vol. 82, no. 11, pp. 1961–1968, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. Cvitanić and I. Karatzas, “Backward stochastic differential equations with reflection and Dynkin games,” The Annals of Probability, vol. 24, no. 4, pp. 2024–2056, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  10. S. Hamadène, “Reflected BSDE's with discontinuous barrier and application,” Stochastics and Stochastics Reports, vol. 74, no. 3-4, pp. 571–596, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  11. I. Karatzas and S. E. Shreve, Methods of Mathematical Finance, vol. 39, Springer, New York, NY, USA, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  12. C. Dellacherie and P. Meyer, Probabilities and Potential, chapter 1–4, Hermann, Paris, France, 1975.
  13. S. Peng, “Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer's type,” Probability Theory and Related Fields, vol. 113, no. 4, pp. 473–499, 1999. View at Publisher · View at Google Scholar · View at MathSciNet