Dynamically consistent risk measures are constructed via optimal transport penalizations of transition laws, yielding generators that are first-order convex Hamiltonians on gradients under linear scaling or second-order convex functionals on Hessians under martingale constraints.
Peng.G-expectation,G-Brownian motion and related stochastic calculus of Itˆ o type
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An optimal transport foundation for a class of dynamically consistent risk measures
Dynamically consistent risk measures are constructed via optimal transport penalizations of transition laws, yielding generators that are first-order convex Hamiltonians on gradients under linear scaling or second-order convex functionals on Hessians under martingale constraints.