Optimal stochastic control of diffusion type processes and Hamilton-Jacobi-Bellman equations

1982 ◽  
pp. 199-215
Author(s):  
P. L. Lions
Keyword(s):  
Stochastic Control ◽  
Optimal Stochastic Control ◽  
Diffusion Type ◽  
Bellman Equations ◽  
Hamilton Jacobi Bellman

scholarly journals Policy iteration for Hamilton–Jacobi–Bellman equations with control constraints

2021 ◽  
Author(s):  
Sudeep Kundu ◽  
Karl Kunisch
Keyword(s):  
Linear Equations ◽  
Hjb Equation ◽  
Policy Iteration ◽  
Optimal Feedback Control ◽  
Iteration Step ◽  
Control Constraints ◽  
Hjb Equations ◽  
Bellman Equations ◽  
Hamilton Jacobi Bellman ◽  
Feedback Control Theory

AbstractPolicy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case. Here we analyze the case with control constraints both for the HJB equations which arise in deterministic and in stochastic control cases. The linear equations in each iteration step are solved by an implicit upwind scheme. Numerical examples are conducted to solve the HJB equation with control constraints and comparisons are shown with the unconstrained cases.

Combined Fixed Point and Policy Iteration for Hamilton--Jacobi--Bellman Equations in Finance

2012 ◽  
Vol 50 (4) ◽  
pp. 1861-1882 ◽  
Author(s):  
Y. Huang ◽  
P. A. Forsyth ◽  
G. Labahn
Keyword(s):  
Fixed Point ◽  
Policy Iteration ◽  
Bellman Equations ◽  
Hamilton Jacobi Bellman
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