Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillators

M. Lauriere, Z. Li, L. Mertz, J. Wylie, S. Zuo, J. Lelong, B. Bouchard, J.-F. Chassagneux, F. Delarue, E. Gobet
2019 ESAIM Proceedings and Surveys  
We consider the optimal stopping and optimal control problems related to stochastic variational inequalities modeling elasto-plastic oscillators subject to random forcing. We formally derive the corresponding free boundary value problems and Hamilton-Jacobi-Bellman equations which belong to a class of nonlinear partial of differential equations with nonlocal Dirichlet boundary conditions. Then, we focus on solving numerically these equations by employing a combination of Howard's algorithm and
more » ... rd's algorithm and the numerical approach [A backward Kolmogorov equation approach to compute means, moments and correlations of non-smooth stochastic dynamical systems; Mertz, Stadler, Wylie; 2017] for this type of boundary conditions. Numerical experiments are given.
doi:10.1051/proc/201965425 fatcat:vfwcmiax2vfsdde3yyxqfw6h4m