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.
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A sensitivity analysis reduces nonlinear Kolmogorov PDEs (nonlinearity from ε-neighborhood max over drifts/diffusions) to a linear PDE plus ε times a second linear PDE, enabling efficient high-dimensional Monte Carlo approximation with error bounds.
Develops robust SGLD with non-asymptotic convergence bounds for non-convex DRO and applies it to neural network regression under adversarial corruption.
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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.
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Numerical method for nonlinear Kolmogorov PDEs via sensitivity analysis
A sensitivity analysis reduces nonlinear Kolmogorov PDEs (nonlinearity from ε-neighborhood max over drifts/diffusions) to a linear PDE plus ε times a second linear PDE, enabling efficient high-dimensional Monte Carlo approximation with error bounds.
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Robust SGLD algorithm for solving non-convex distributionally robust optimisation problems
Develops robust SGLD with non-asymptotic convergence bounds for non-convex DRO and applies it to neural network regression under adversarial corruption.