Stochastic ordering by g-expectations

TL;DR

This paper establishes conditions for comparing diffusion processes under nonlinear g-expectations, with applications to financial claim pricing and portfolio constraints.

Contribution

It introduces new comparison criteria for g-stochastic ordering using FBSDEs and PDEs, extending existing convexity and monotonicity results.

Findings

Derived sufficient conditions for convex and monotonic g-stochastic ordering.

Extended comparison results for solutions of FBSDEs and PDEs.

Applied theoretical results to contingent claim pricing under portfolio constraints.

Abstract

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.