Numerical Approximation of a System of Hamilton–Jacobi–Bellman Equations Arising in Innovation Dynamics
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In: Journal of Scientific Computing , Vol. 92.2022, 54, 04.07.2022, p. 92.2022.
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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 -