An optimal finite-time horizon feedback control problem for (semi-linear) wave equations is presented. The feedback law can be derived from the dynamic programming principle and requires to solve the evolutionary Hamilton-Jacobi-Bellman (HJB) equation. Classical discretization methods based on finite elements lead to approximated problems governed by ODEs in high dimensional spaces which makes ...

This note is devoted to stabilizing a coupled PDE–ODE system with interaction at the interface. First, a state feedback boundary controller is designed, and the system is transformed into an exponentially stable PDE–ODE cascadewith an invertible integral transformation,where PDE backstepping is employed. Moreover, the solution to the resulting closed-loop system is derived explicitly. Second, a...

A continuous time mean-variance (MV) problem optimizes the bi-objective criteria 5 (V, E), respectively representing variance V and expected value E of a random variable at the end 6 of a time horizon T . This problem is computationally challenging since the dynamic programming 7 principle cannot be directly applied to the variance criterion. An embedding technique has been 8 proposed in [18, 2...

We study the exploratory Hamilton–Jacobi–Bellman (HJB) equation arising from entropy-regularized control problem, which was formulated by Wang, Zariphopoulou, and Zhou (J. Mach. Learn. Res., 21 (2020), 198) in context of reinforcement learning continuous time space. establish well-posedness regularity viscosity solution to equation, as well convergence problem classical stochastic when level ex...

In this article we propose a $\alpha$-hypergeometric model with uncertain volatility (UV) where derive worst-case scenario for option pricing. The approach is based on the connexion between certain class of nonlinear partial differential equations HJB-type (G-HJB equations), that govern expectation UV and provide an alternative to difficult calibration problem models, second-order backward stoc...

The illiquid market model HJB equations and characterization of the solution Power utility functions and numerical results

We study the stochastic Hamilton–Jacobi–Bellman (HJB) equation with jump, which arises from a non-Markovian optimal control problem recursive utility cost functional. The solution to is predictable triplet of random fields. show that value function problem, under some regularity assumptions, HJB equation; and classical this characterizes control. With additional assumptions on coefficients, an ...

A stochastic Ramsey model is studied with the Cobb-Douglas production function maximizing the expected discounted utility of consumption. We transformed the Hamilton-Jacobi-Bellman (HJB) equation associated with the stochastic Ramsey model so as to transform the dimension of the state space by changing the variables. By the viscosity solution method, we established the existence of viscosity so...