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Article

Non-Linear Time-Advanced Backward Stochastic Partial Differential Equations With Jumps

Pages 673-700 | Received 11 Mar 2014, Accepted 27 Mar 2015, Published online: 24 Jun 2015

References

  • Duffe, D., and Epstein, M. 1992. Stochastic differential utility. Econometrica 60:353–394.
  • Karoui, N.E., Peng, S., and Quenez, M.C. 1997. Backward stochastic differential equations in finance. Mathematical Finance 7:1–77.
  • Menoukeu-Pamen, O., Meyer-Brandis, T., Proske, F., and Binti-Salleh, H. 2013. Malliavin calculus applied to optimal control of stochastic partial differential equations with jumps. Stochastics 85:431–463.
  • Ma, J., Protter, P., and Yong, J. 1994. Solving forward-backward stochastic differential equations explicitly: a four step scheme. Probability Theory and Related Fields 98:339–359.
  • Øksendal, B. and Sulem, A. 2009. Applied Stochastic Control of Jump Diffusions, 3rd ed. Berlin: Springer.
  • Yong, J., and Zhou, X. 1999. Stochastic Controls: Hamiltonian Systems and HJB Equations. New York: Springer.
  • Pardoux, E., and Peng, S. 1990. Adapted solution of a backward stochastic differential equation. Systems Control Letter 14:55–61.
  • Barles, G., Buckdahn, R., and Pardoux, E. 1997. Backward stochastic differential equations and integral partial differential equations. Stochastics and Stochastics Reports 60: 57–83.
  • Situ, R. 1997. On strong solution backward stochastic differential equations with jumps and applications. Stochastic Process. Appl. 66:209–236.
  • Peng, S., and Yang, Z. 2009. Anticipated backward stochastic differential equations. Annals of Probability 37:877–902.
  • Chen, L., and Wu, Z. 2010. Maximum principle for the stochastic optimal control problem with delay and application. Automatica 46:1074–1080.
  • Menoukeu-Pamen, O. 2013. Optimal control for stochastic delay systems under model uncertainty: A stochastic differential game approach. Journal of Optimization Theory and Applications. DOI: 10.1007/s10957-013-0484-4
  • Øksendal, B., Sulem, A., and Zhang, T. 2011. Optimal control of stochastic delay equations and time-advanced backward stochastic differential equations. Advances in Applied Probability 43:572–596.
  • Shi, J.T. 2012. Maximum principle of recursive optimal control problem for forward–backward stochastic delayed system with Poisson jumps. Scientia Sinica Mathematica 43:251–270.
  • Hassani, M., and Ouknine, Y. 2002. Infinite dimensional BSDE with jumps. Stochastic Analysis and Applications 20:519–565.
  • Hu, Y., Ma, J., and Yong, J. 1999. On semi-linear degenerate backward stochastic partial differential equations. Probability Theory and Related Fields 113:135–170.
  • Hu, Y., and Peng, S. 1990. Maximum principle for semilinear stochastic evolution control systems. Stochastics and Stochastics Reports 33:159–180.
  • Hu, Y., and Peng, S. 1991. Adapted solution of a backward semilinear stochastic evolution equation. Stochastic Analysis and Applications 9:445–459.
  • Mahmudov, N., and McKibben, M. 2007. On backward stochastic evolution equations in Hilbert spaces and optimal control. Nonlinear Analysis: Theory Methods & Applications 67: 1260–1274.
  • Øksendal, B., Proske, F., and Zhang, T. 2005. Backward stochastic partial differential equations with jumps and application to optimal control of random jump fields. Stochastic: An International Journal of Probability and Stochastic Processes 77:381–399.
  • Tessitore, G. 1996. Existence, uniqueness and space regularity of the adapted solutions of a backward SPDE. Stochastic Analysis and Applications 14:461–486.
  • Øksendal, B., Sulem, A., and Zhang, T. 2012. Optimal partial information control of spdes with delay and time-advanced backward spdes. In Stochastic Analysis and Applications to Finance: Essays in Honour of Jia-an Yan, vol. 33, T. Zhang and X. Zhou, Eds. Interdisciplinary Mathematical Sciences. Singapore: World Scientific Publishing, 355–384.
  • Bensousssan, A. 1983. Maximum principle and dynamic programming approaches of the optimal control of partially observed diffusions. Stochastics and Stochastics Reports 9:169–222.
  • Caraballo, T., Liu, K., and Truman, A. 2000. Stochastic functional partial differential equations: existence, uniqueness and asymptotic decay property. Proc. R. Soc. Lond. A 456:1775–1802.
  • Prato, G.D., and Zabczyk, J. 1993. Stochastic Equations in Infinite Dimensions. Cambridge, UK: Cambridge University Press.
  • Kallianpur, G., and Xiong, J. 1995. Stochastic Differential Equations in Infinite Dimensional Spaces. vol. 33. IMS Lecture Notes-Monograph Series. Hayward, CA: Institute of Mathematical Statistics.
  • Pardoux, E., and Peng, S. 1979. Stochastic partial differential equations and filtering of diffusion processes. Stochastics and Stochastics Reports 3:127–167.
  • Peszat, S., and Zabczyk, J. 2007. Stochastic Partial Differential Equations with Lévy Noise. Cambridge, UK: Cambridge University Press.
  • Zhang, X. 2009. On stochastic evolution equations with non-Lipschitz coefficients. Stochastics and Dynamics 9:549–595.
  • Prévôt, C., and Röckner, M. 2007. A Concise Course on Stochastic Partial Differential Equations. Lecture Notes in Mathematics. Berlin: Springer Berlin.
  • Briand, P., Delyon, B., Hu, Y., Pardoux, E., and Stoica, L. 2003. lp solutions of backward stochastic differential equations. Stochastic Processes and Applications 108:109–129.

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