Policy Iteration Algorithm for Singular Controlled Diffusion Processes

Abstract The estimates of N. V. Krylov for distributions of stochastic integrals by means of the L d {L_{d}} -norm of a measurable function are well-known and are widely used in the theory of stochastic differential equations and controlled diffusion processes. We generalize estimates of this type for optional semimartingales, then apply these estimates to prove the change of variables formula for a general class of functions from the Sobolev space W d 2 {W^{2}_{d}} . We also show how to use these estimates for the investigation of L 2 {L^{2}} -convergence of solutions of optional SDE’s.

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On time-inhomogeneous controlled diffusion processes in domains

The Annals of Probability ◽

10.1214/009117906000000395 ◽

2007 ◽

Vol 35 (1) ◽

pp. 206-227 ◽

Cited By ~ 5

Author(s):

Hongjie Dong ◽

N. V. Krylov

Keyword(s):

Diffusion Processes ◽

Controlled Diffusion ◽

Controlled Diffusion Processes

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Adaptive Kernel-Width Selection for Kernel-Based Least-Squares Policy Iteration Algorithm

Advances in Neural Networks – ISNN 2011 - Lecture Notes in Computer Science ◽

10.1007/978-3-642-21090-7_70 ◽

2011 ◽

pp. 611-619

Author(s):

Jun Wu ◽

Xin Xu ◽

Lei Zuo ◽

Zhaobin Li ◽

Jian Wang

Keyword(s):

Least Squares ◽

Policy Iteration ◽

Iteration Algorithm ◽

Kernel Width ◽

Adaptive Kernel ◽

Policy Iteration Algorithm ◽

Selection For

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A policy iteration algorithm for nonzero-sum stochastic impulse games

ESAIM Proceedings and Surveys ◽

10.1051/proc/201965027 ◽

2019 ◽

Vol 65 ◽

pp. 27-45

Author(s):

René Aïd ◽

Francisco Bernal ◽

Mohamed Mnif ◽

Diego Zabaljauregui ◽

Jorge P. Zubelli

Keyword(s):

Nash Equilibrium ◽

Numerical Methods ◽

Variational Inequalities ◽

Convergence Analysis ◽

Policy Iteration ◽

Iteration Algorithm ◽

Value Functions ◽

Numerical Tests ◽

Wide Range ◽

Policy Iteration Algorithm

This work presents a novel policy iteration algorithm to tackle nonzero-sum stochastic impulse games arising naturally in many applications. Despite the obvious impact of solving such problems, there are no suitable numerical methods available, to the best of our knowledge. Our method relies on the recently introduced characterisation of the value functions and Nash equilibrium via a system of quasi-variational inequalities. While our algorithm is heuristic and we do not provide a convergence analysis, numerical tests show that it performs convincingly in a wide range of situations, including the only analytically solvable example available in the literature at the time of writing.

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