  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.
