SMOOTH FIT PRINCIPLE FOR IMPULSE CONTROL OF MULTIDIMENSIONAL DIFFUSION PROCESSES

被引：34

作者：

Guo, Xin ^{[1
]}

Wu, Guoliang ^{[2
]}

机构：

[1] Univ Calif Berkeley, Dept Ind Engn & Operat Res, Berkeley, CA 94720 USA

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2009年 / 48卷 / 02期

关键词：

stochastic impulse control; viscosity solution; quasi-variational inequality; smooth fit; controlled diffusion; VISCOSITY SOLUTIONS; STOCHASTIC-CONTROL; SINGULAR CONTROL; INTERVENTION; OPTIMIZATION; INVENTORY; POLICIES;

D O I：

10.1137/080716001

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Value functions of impulse control problems are known to satisfy quasi-variational inequalities (QVIs) [A. Bensoussan and J.-L. Lions, Impulse Control and Quasivariational Inequalities, Heyden & Son, Philadelphia, 1984; translation of Controle Impulsionnel et Inequations Quasi Variationnelles, Gauthier-Villars, Paris, 1982]. This paper proves the smooth-fit C-1 property of the value function for multidimensional controlled diffusions, using a viscosity solution approach. We show by examples how to exploit this regularity property to derive explicitly optimal policy and value functions.

引用

页码：594 / 617

页数：24

共 38 条

[21] Discounted robust control for Markov diffusion processes
Daniel Lopez-Barrientos, Jose
Jasso-Fuentes, Hector
Adriana Escobedo-Trujillo, Beatris
TOP, 2015, 23 (01) : 53 - 76
[22] Optimal Control of Diffusion Processes with Terminal Constraint in Law
Samuel Daudin
Journal of Optimization Theory and Applications, 2022, 195 : 1 - 41
[23] A New Model of Continuous-Time Markov Processes and Impulse Stochastic Control
Cao, Xi-Ren
PROCEEDINGS OF THE 48TH IEEE CONFERENCE ON DECISION AND CONTROL, 2009 HELD JOINTLY WITH THE 2009 28TH CHINESE CONTROL CONFERENCE (CDC/CCC 2009), 2009, : 525 - 530
[24] Optimal variational principle for backward stochastic control systems associated with Levy processes
Tang MaoNing
Zhang Qi
SCIENCE CHINA-MATHEMATICS, 2012, 55 (04) : 745 - 761
[25] Impulse Stochastic Control for the Optimization of the Dividend Payments of the Compound Poisson Risk Model Perturbed by Diffusion
Zhang, Shuaiqi
STOCHASTIC ANALYSIS AND APPLICATIONS, 2012, 30 (04) : 642 - 661
[26] Optimal variational principle for backward stochastic control systems associated with Lévy processes
MaoNing Tang
Qi Zhang
Science China Mathematics, 2012, 55 : 745 - 761
[27] Optimal variational principle for backward stochastic control systems associated with Lévy processes
TANG MaoNing 1 & ZHANG Qi 2
2 School of Mathematical Sciences
Science China(Mathematics), 2012, 55 (04) : 741 - 757
[28] Performance Analysis for Operational Optimal Control for Complex Industrial Processes - the Square Impact Principle
Wang, Aiping
Wang, Hong
Sheng, Ning
Yin, Xin
2015 21ST INTERNATIONAL CONFERENCE ON AUTOMATION AND COMPUTING (ICAC), 2015, : 15 - 20
[29] Optimal insurance control for insurers with jump-diffusion risk processes
Tian, Linlin
Bai, Lihua
ANNALS OF ACTUARIAL SCIENCE, 2019, 13 (01) : 198 - 213
[30] Ergodic Control, Bias, and Sensitive Discount Optimality for Markov Diffusion Processes
Jasso-Fuentes, Hector
Hernandez-Lerma, Onesimo
STOCHASTIC ANALYSIS AND APPLICATIONS, 2009, 27 (02) : 363 - 385

← 1 2 3 4 →