\( G\)-expectation approach to stochastic ordering. (English) Zbl 1500.91137
Summary: 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.
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 60E15 | Inequalities; stochastic orderings |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 60G65 | Nonlinear processes (e.g., \(G\)-Brownian motion, \(G\)-Lévy processes) |
Keywords:
stochastic ordering; sublinear expectation; \( G \)-expectation; nonlinear expectation; \( G \)-Brownian motion; \( G \)-forward-backward SDE; increasing order; convex order; convexity; monotonicityReferences:
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