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Quadratic g-convexity, C-convexity and their relationships

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  • Jia, Guangyan
  • Zhang, Na

Abstract

In this paper we study Jensen’s inequality under quadratic g-expectation, i.e., the expectation generated by backward stochastic differential equations (BSDEs) with generator of quadratic growth in its component z. In particular, we define a new kind of convexity, the C-convexity, via a second order ODE depending on a real constant C, and we study the relationships between quadratic g-convexity and C-convexity.

Suggested Citation

  • Jia, Guangyan & Zhang, Na, 2015. "Quadratic g-convexity, C-convexity and their relationships," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2272-2294.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:6:p:2272-2294
    DOI: 10.1016/j.spa.2014.12.012
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    References listed on IDEAS

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    1. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    2. Briand, Philippe & Elie, Romuald, 2013. "A simple constructive approach to quadratic BSDEs with or without delay," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 2921-2939.
    3. Tevzadze, Revaz, 2008. "Solvability of backward stochastic differential equations with quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 503-515, March.
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