Nonlinear Expectations, Nonlinear Evaluations and Risk Measures

Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1856)

Abstract

  • 1. Introduction
    • 1.1. Searching the Mechanism of Evaluations of Risky Assets

    • 1.2. Axiomatic Assumptions for Evaluations of Derivatives

    • 1.3. Organization of the Lecture

  • 2. Brownian Filtration Consistent Evaluations and Expectations
  • 3. Backward Stochastic Differential Equations: g-Evaluations and g-Expectations
    • 3.1. BSDE: Existence, Uniqueness and Basic Estimates

    • 3.2. 1-Dimensional BSDE

    • 3.3. A Monotonic Limit Theorem of BSDE

    • 3.4. g-Martingales and (Nonlinear) g-Supermartingale Decomposition Theorem

  • 4. Finding the Mechanism: Is an Open image in new window -Expectation a g-Expectation?
  • 5. Dynamic Risk Measures

  • 6. Numerical Solution of BSDEs: Euler’s Approximation

  • 7. Appendix
    • 7.1. Martingale Representation Theorem

    • 7.2. A Monotonic Limit Theorem of Itô’s Processes

    • 7.3. Optional Stopping Theorem for Open image in new window -Supermartingale

  • References

  • References on BSDE and Nonlinear Expectations

Mathematics Subject Classification (2000):

60G99 60-06 91-06 91B06 91B16 91B24 91B28 91B30 91B70 93-06 93E11 93E20 

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Institute of MathematicsShandong UniversityJinanPeople’s Republic of China

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