# American Institute of Mathematical Sciences

March  2021, 6(1): 61-98. doi: 10.3934/puqr.2021004

## Stochastic ordering by g-expectations

 School of Physical and Mathematical Sciences, Division of Mathematical Sciences, Nanyang Technological University, Singapore 637371

Email: lysel001@e.ntu.edu.sg, nprivault@ntu.edu.sg

Received  October 31, 2019 Accepted  January 06, 2021 Published  March 2021

Fund Project: This research is supported by the Ministry of Education, Singapore (Grant No. MOE2018-T1-001-201)

We derive sufficient conditions for the convex and monotonic g-stochastic ordering of diffusion processes under nonlinear g-expectations and g-evaluations. Our approach relies on comparison results for forward-backward stochastic differential equations and on several extensions of convexity, monotonicity, and continuous dependence properties for the solutions of associated semilinear parabolic partial differential equations. Applications to contingent claim price comparison under different hedging portfolio constraints are provided.

Citation: Sel Ly, Nicolas Privault. Stochastic ordering by g-expectations. Probability, Uncertainty and Quantitative Risk, 2021, 6 (1) : 61-98. doi: 10.3934/puqr.2021004
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