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Existence and Non-uniqueness of Solutions for BSDE

  • Xiaobo Bao
  • Freddy Delbaen
  • Ying Hu

Abstract

We study BSDE where the driver is pathwise quadratically bounded. The associated utility function is always a solution but even in the class of Markovian solutions uniqueness is not guaranteed. we relate the problem to problems for quasi-linear parabolic PDE.

Keywords

Stochastic Differential Equation Predictable Process Exponential Moment Backward Stochastic Differential Equation Density Process 
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References

  1. 1.
    Bao, X.: Backward stochastic differential equations with super-quadratic growth. Ph.D. thesis, ETH-Zurich (2009) Google Scholar
  2. 2.
    Bion-Nadal, J.: Time consistent dynamic risk processes. Stoch. Process. Appl. 119(2), 633–654 (2009) MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Delbaen, F., Peng, S., Rosazza-Gianin, E.: Representation of the penalty term of dynamic concave utilities. Finance Stoch., accepted (2009) Google Scholar
  4. 4.
    Kazamaki, N.: Continuous Exponential Martingales and BMO. Lecture Notes in Mathematics, vol. 1579. Springer, Berlin (1994) zbMATHGoogle Scholar
  5. 5.
    Phelps, R.R.: Convex Functions, Monotone Operators and Differentiability. Lecture Notes in Mathematics, vol. 1364, 2nd edn. Springer, Berlin (1993) zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of MathematicsETH ZurichZurichSwitzerland
  2. 2.Département de MathématiquesUniversité de Rennes-1RennesFrance

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