scholarly journals Some Non-monotone Schemes for Time Dependent Hamilton–Jacobi–Bellman Equations in Stochastic Control

2015 ◽  
Vol 66 (3) ◽  
pp. 1122-1147 ◽  
Author(s):  
Xavier Warin
Keyword(s):  
Stochastic Control ◽  
Time Dependent ◽  
Bellman Equations ◽  
Monotone Schemes ◽  
Hamilton Jacobi Bellman

scholarly journals Some non monotone schemes for Hamilton-Jacobi-Bellman equations

2019 ◽  
Vol 65 ◽  
pp. 476-497
Author(s):  
Xavier Warin
Keyword(s):  
Viscosity Solution ◽  
Discrete Problem ◽  
Numerical Schemes ◽  
Bellman Equations ◽  
Monotone Schemes ◽  
Hamilton Jacobi Bellman

We extend the theory of Barles Jakobsen [3] for a class of almost monotone schemes to solve stationary Hamilton Jacobi Bellman equations. We show that the monotonicity of the schemes can be relaxed still leading to the convergence to the viscosity solution of the equation even if the discrete problem can only be solved with some error. We give some examples of such numerical schemes and show that the bounds obtained by the framework developed are not tight. At last we test the schemes.

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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