What question did this study set out to answer?

To investigate classical solvability for second-order Hamilton-Jacobi-Bellman equations in stochastic optimal control contexts.

December 22, 2025Open Access

Classical solution to second-order Hamilton-Jacobi-Bellman equation and optimal feedback control for linear-convex problem

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The paper demonstrates the unique solution to HJB equations in convex stochastic control, highlighting optimal control properties.

To investigate classical solvability for second-order Hamilton-Jacobi-Bellman equations in stochastic optimal control contexts.
Introduced Hamiltonian system for analysis
Used gradient descent in Hilbert space settings
Demonstrated existence and uniqueness of optimal control
Proven connections between Hamiltonian system and value function
Applied dynamic programming principles for validation.
Established regularity of solutions for the Hamiltonian system
Showed unique classical solutions for HJB equations
Verified optimal feedback control through value function properties

Li et al. (2025) studied this question.

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