Stochastic Optimal Control Problem in Advertising Model with Delay

Mohammed S E A, Stochastic differential equations with memory: Theory, examples and applications, Progress in Probability, Stochastic Analysis and Related Topics 6, The Geido Workshop, Birkhäuser, 1998.

Arriojas M, Hu Y, Mohammed S E A, et al., A delayed Black and Scholes formula, Stochastic Analysis and Applications, 2007, 25: 471–492.

Øksendal B and Sulem A, A maximum principle for optimal control of stochastic systems with delay, with application to finance, Eds. by Menaldi J M, Rofman E, and Sulem A, Optimal Control and Partial Differential Equations, ISO Press, Amsterdam, 2000, 64–79.

Øksendal B and Sulem A, Optimal stochastic impulse control with delayed reaction, Applied Mathematics and Optimization, 2008, 58: 243–255.

Chen L and Wu Z, Maximum principle for the stochastic optimal control problem with delay and application, Automatica, 2010, 46: 1074–1080.

Larssen B, Dynamic programming in stochastic control of systems with delay, Stochastics and Stochastics Reports, 2002, 74: 651–673.

Gozzi F and Marinelli C, Stochastic optimal control of delay equations arising in advertising models, Stochastic Partial Differential Equations and Applications-VII. Lecture Notes in Pure and Applied Mathematics, 2006, 245: 133–148.

Vidale M L and Wolfe H B, An operations research study of sales response to advertising, Operation Research, 1957, 5(3): 370–381.

Nerlove M and Arrow J K, Optimal advertising policy under dynamic conditions, Economica, 1962, 29: 129–142.

Feichtinger G, Hartl R, and Sethi S, Dynamical optimal control models in advertising: Recent developments, Management Science, 1994, 40(2): 195–226.

Gozzi F, Marinelli C, and Savin S, On controlled linear diffusions with delay in a model of optimal advertising under uncertainty with memory effects, Journal of Optimization Theory and Application, 2009, 142: 291–321.

Hu Y and Peng S, Maximum principle for semilinear stochastic evolution control systems, Stochastic and Stochastic Reports, 1990, 33: 159–180.

Ichikawa A, Stability of semilinear stochastic evolution equations, Journal of Mathetical Analysis and Applications, 1982, 90(1): 12–44.

Vinter R B and Kwong R H, The infinite time quadratic control problem for linear systems with state and control delays: An evolution equation approach, SIAM Journal on Control & Optimization, 1981, 19(1): 139–153.

Chojnowska-Michalik A, Representation theorem for general stochastic delay equations, Social Psychology Quarterly, 1978, 26(7): 635–642.

Da Prato G and Zabczyk J, Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge, 1992.

Carton H, Cours de Calcul Différentiel, Nouveau triage, Herman, 2007.

Ekeland I and Témam R, Convex Analysis and Variational Problems, SIAM, Philadelphia, 1999.

Yong J and Zhou X, Stochastic Controls-Hamiltonian Systems and HJB Equation, SpringerVerlag, New York, 1999.

Fuhrman M and Tessitore G, Generalized directional gradients, backward stochastic differential equations and mild solutions of semilinear paraboloc equations, Applied Mathematics and Optimization, 2005, 51(3): 279–332.