Stochastic Optimal Control Problem in Advertising Model with Delay

被引：13

作者：

Chen Li ^{[1
]}

Wu Zhen ^{[2
]}

机构：

[1] China Univ Min & Technol, Sch Sci, Beijing 100083, Peoples R China

[2] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

来源：

JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2020年 / 33卷 / 04期

关键词：

Advertising model; maximum principle; stochastic evolution equation; stochastic optimal control; time-delay system;

D O I：

10.1007/s11424-020-8185-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper investigates the optimal control problem arising in advertising model with delay. The authors reformulate the problem in Hilbert space by stochastic evolution equation and consider the optimal control problem of controlled stochastic evolution system. The necessary and sufficient optimality conditions of the control are established. The proposed approach is different from most existing studies of optimal advertising policy problem with delay. These results are applied to the optimal advertising policy problem under two different structures and the optimal advertising strategies are obtained.

引用

页码：968 / 987

页数：20

共 20 条

[1]

[Anonymous], 1999, Convex Analysis and Variational Problems

[2] A delayed Black and Scholes formula [J].

Arriojas, Mercedes ;

Hu, Yaozhong ;

Mohammed, Salah-Eldin ;

Pap, Gyula .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2007, 25 (02) :471-492

[3]

Carton H, 2007, COURS CALCUL DIFFERE

[4] Maximum principle for the stochastic optimal control problem with delay and application [J].

Chen, Li ;

Wu, Zhen .

AUTOMATICA, 2010, 46 (06) :1074-1080

[5]

CHOJNOWSKAMICHALIK A, 1978, B ACAD POL SCI SMAP, V26, P635

[6]

DA PRATO G., 2014, Encyclopedia of mathematics and its applications, DOI DOI 10.1017/CBO9781107295513

[7] DYNAMIC OPTIMAL-CONTROL MODELS IN ADVERTISING - RECENT DEVELOPMENTS [J].

FEICHTINGER, G ;

HARTL, RF ;

SETHI, SP .

MANAGEMENT SCIENCE, 1994, 40 (02) :195-226

[8] Generalized directional gradients, backward stochastic differential equations and mild solutions of semilinear parabolic equations [J].

Fuhrman, M ;

Tessitore, G .

APPLIED MATHEMATICS AND OPTIMIZATION, 2005, 51 (03) :279-332

[9] On Controlled Linear Diffusions with Delay in a Model of Optimal Advertising under Uncertainty with Memory Effects [J].

Gozzi, F. ;

Marinelli, C. ;

Savin, S. .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2009, 142 (02) :291-321

[10]

Gozzi F., 2006, Stochastic Partial Differential Equations and Applications---VII, V245, P133

← 1 2 →