arXiv published a paper on the differentiability and convexity of solution maps for fully nonlinear parabolic HJB equations.
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Jean-François Chassagneux, Stéphane Crépey, Grégoire Loeper, and Justin Ruelland published an academic paper on arXiv focusing on the dependence of solutions to fully nonlinear parabolic Hamilton-Jacobi-Bellman (HJB) equations on finite-dimensional terminal conditions, with research motivation derived from the dual formulation of semimartingale optimal transport. Based on Evans-Krylov theory, combined with partial differential equation arguments and probabilistic representation methods, the study proves the continuous directional differentiability of the solution map and local strong convexity under point evaluation, and extends relevant conclusions to cascaded Cauchy problem scenarios coupled with multi-time terminal conditions.
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- arXiv q-finDifferentiability and Convexity of Solution Maps for Fully Nonlinear Parabolic HJB Equations
This study focuses on the dependence of solutions to fully nonlinear parabolic Hamilton-Jacobi-Bellman (HJB) equations on finite-dimensional terminal conditions, motivated by the dual formulation of optimal transport for semimartingales. Based on Evans-Krylov theory and combining PDE arguments with probabilistic representation methods, the study proves continuous directional differentiability and local strong convexity under point evaluation of the solution map, and extends the results to cascaded Cauchy problems with multiple coupled terminal times.
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