TY - JOUR

T1 - Numerical Approximation of a System of Hamilton–Jacobi–Bellman Equations Arising in Innovation Dynamics

AU - Banas, Lubomir

AU - Dawid, Herbert

AU - Randrianasolo, Tsiry Avisoa

AU - Storn, Johannes

AU - Wen , Xingang

PY - 2022/7/4

Y1 - 2022/7/4

N2 - 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.

AB - 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.

U2 - 10.1007/s10915-022-01892-x

DO - 10.1007/s10915-022-01892-x

M3 - Article

VL - 92.2022

SP - 92.2022

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

SN - 0885-7474

M1 - 54

ER -