Numerical Approximation of a System of Hamilton–Jacobi–Bellman Equations Arising in Innovation Dynamics

• Main Authors: Baňas, L. (Author), Dawid, H. (Author), Randrianasolo, T.A (Author), Storn, J. (Author), Wen, X. (Author)
• Format: Article
• Language: English
• Published: Springer 2022
• Subjects: Adaptive mesh refinement; Collocation method; Dynamic programming; Finite difference approximations; Finite difference method; Finite element method; Hamilton Jacobi Bellman equation; Hamilton–Jacobi–Bellman equations; Innovation dynamics; Least squares approximations; Least squares finite element methods; Least-squares finite element method; Nonlinear equations; Numerical approximations; Numerical methods; Partial differential equations; Stabilized finite element; Stabilized finite element method; Stochastic game; Stochastic games; Stochastic systems
• Online Access: View Fulltext in Publisher
• ISBN: 08857474 (ISSN)
• DOI: 10.1007/s10915-022-01892-x

We consider a system of fully nonlinear partial differential equations that corresponds to the Hamilton–Jacobi–Bellman equations for the value functions of an optimal innovation investment problem of a monopoly firm facing bankruptcy risk. We compare several algorithms for the numerical solution of the considered problem: the collocation method, the finite difference method, WENO method and the adaptive finite element method. We discuss implementation issues for the considered schemes and perform numerical studies for different model parameters to assess their performance. © 2022, The Author(s).