scholarly journals A Fixed-Point Policy-Iteration-Type Algorithm for Symmetric Nonzero-Sum Stochastic Impulse Control Games

2019 ◽  
Author(s):  
Diego Zabaljauregui
Keyword(s):  
Fixed Point ◽  
Impulse Control ◽  
Policy Iteration ◽  
Stochastic Impulse Control ◽  
Type Algorithm

scholarly journals A Fixed-Point Policy-Iteration-Type Algorithm for Symmetric Nonzero-Sum Stochastic Impulse Control Games

2020 ◽  
Author(s):  
Diego Zabaljauregui
Keyword(s):  
Fixed Point ◽  
Impulse Control ◽  
Strong Dependence ◽  
Policy Iteration ◽  
Initial Guess ◽  
Previous Method ◽  
Modelling Framework ◽  
Symmetric Games ◽  
Type Algorithm ◽  
Analytical Approaches

Abstract Nonzero-sum stochastic differential games with impulse controls offer a realistic and far-reaching modelling framework for applications within finance, energy markets, and other areas, but the difficulty in solving such problems has hindered their proliferation. Semi-analytical approaches make strong assumptions pertaining to very particular cases. To the author’s best knowledge, the only numerical method in the literature is the heuristic one we put forward in Aïd et al (ESAIM Proc Surv 65:27–45, 2019) to solve an underlying system of quasi-variational inequalities. Focusing on symmetric games, this paper presents a simpler, more precise and efficient fixed-point policy-iteration-type algorithm which removes the strong dependence on the initial guess and the relaxation scheme of the previous method. A rigorous convergence analysis is undertaken with natural assumptions on the players strategies, which admit graph-theoretic interpretations in the context of weakly chained diagonally dominant matrices. A novel provably convergent single-player impulse control solver is also provided. The main algorithm is used to compute with high precision equilibrium payoffs and Nash equilibria of otherwise very challenging problems, and even some which go beyond the scope of the currently available theory.

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

Stochastic Impulse Control with Regime-Switching Dynamics

2015 ◽  
Author(s):  
Ralf Korn ◽  
Yaroslav Melnyk ◽  
Frank Thomas Seifried
Keyword(s):  
Regime Switching ◽  
Impulse Control ◽  
Stochastic Impulse Control ◽  
Switching Dynamics

scholarly journals Stochastic Impulse Control of Non-Markovian Processes

2009 ◽  
Vol 61 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Boualem Djehiche ◽  
Said Hamadène ◽  
Ibtissam Hdhiri
Keyword(s):  
Impulse Control ◽  
Markovian Processes ◽  
Stochastic Impulse Control

Stochastic impulse control with regime-switching dynamics

2017 ◽  
Vol 260 (3) ◽  
pp. 1024-1042 ◽  
Author(s):  
Ralf Korn ◽  
Yaroslav Melnyk ◽  
Frank Thomas Seifried
Keyword(s):  
Regime Switching ◽  
Impulse Control ◽  
Stochastic Impulse Control ◽  
Switching Dynamics

scholarly journals On the Optimal Stochastic Impulse Control of Linear Diffusions

2008 ◽  
Vol 47 (2) ◽  
pp. 703-732 ◽  
Author(s):  
Luis H. R. Alvarez ◽  
Jukka Lempa
Keyword(s):  
Impulse Control ◽  
Stochastic Impulse Control ◽  
Linear Diffusions

Optimal stochastic impulse control with random coefficients and execution delay

Stochastics ◽  
2017 ◽  
Vol 90 (2) ◽  
pp. 151-164
Author(s):  
Ibtissam Hdhiri ◽  
Monia Karouf
Keyword(s):  
Impulse Control ◽  
Random Coefficients ◽  
Stochastic Impulse Control ◽  
Execution Delay

scholarly journals Inertial Mann-Type Algorithm for a Nonexpansive Mapping to Solve Monotone Inclusion and Image Restoration Problems

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 750
Author(s):  
Natthaphon Artsawang ◽  
Kasamsuk Ungchittrakool
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Image Restoration ◽  
Zero Point ◽  
Monotone Operators ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Type Method ◽  
Type Algorithm ◽  
Inertial Terms

In this article, we establish a new Mann-type method combining both inertial terms and errors to find a fixed point of a nonexpansive mapping in a Hilbert space. We show strong convergence of the iterate under some appropriate assumptions in order to find a solution to an investigative fixed point problem. For the virtue of the main theorem, it can be applied to an approximately zero point of the sum of three monotone operators. We compare the convergent performance of our proposed method, the Mann-type algorithm without both inertial terms and errors, and the Halpern-type algorithm in convex minimization problem with the constraint of a non-zero asymmetric linear transformation. Finally, we illustrate the functionality of the algorithm through numerical experiments addressing image restoration problems.

A General Verification Result for Stochastic Impulse Control Problems

2017 ◽  
Vol 55 (2) ◽  
pp. 627-649 ◽  
Author(s):  
Christoph Belak ◽  
Sören Christensen ◽  
Frank Thomas Seifried
Keyword(s):  
Impulse Control ◽  
Control Problems ◽  
Stochastic Impulse Control
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