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$ G $-expectation approach to stochastic ordering

  • * Corresponding author: Nicolas Privault

    * Corresponding author: Nicolas Privault
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  • This paper studies stochastic ordering under nonlinear expectations $ {\mathcal E}_{\mathcal{G}} $ generated by solutions of $ G $-Backward Stochastic Differential Equations ($ G $-BSDEs) defined on $ G $-expectation spaces. We derive sufficient conditions for the convex, increasing convex, and monotonic $ G $-stochastic orderings of $ G $-diffusion processes at terminal time. Our approach relies on comparison properties for $ G $-Forward-Backward Stochastic Differential Equations ($ G $-FBSDEs) and on relevant extensions of convexity, monotonicity and continuous dependence properties for the solutions of associated Hamilton-Jacobi-Bellman (HJB) equations. Applications of $ G $-stochastic ordering to contingent claim superhedging price comparison under ambiguous coefficients are provided.

    Mathematics Subject Classification: Primary: 60E15; Secondary: 35B51, 60H10, 60H30.


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