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Mohammed, S.-E.A. (1998) Stochastic Differential Systems with Memory: Theory, Examples and Applications. In: Decreusefond, L., Øksendal, B., Gjerde, J. and Üstünel, A.S., Eds., Stochastic Analysis and Related Topics VI, Birkhäuser Boston, 1-77.
https://doi.org/10.1007/978-1-4612-2022-0_1

has been cited by the following article:

• TITLE: Stochastic Maximum Principle for Optimal Advertising Models with Delay and Non-Convex Control Spaces

  AUTHORS: Giuseppina Guatteri, Federica Masiero

  KEYWORDS: Stochastic Optimal Control, Delay Equations, Advertisement Models, Stochastic Maximum Principle

  JOURNAL NAME: Advances in Pure Mathematics, Vol.14 No.6, June 18, 2024

  ABSTRACT: In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we let the dynamics of the product goodwill to depend on the past, and also on past advertising efforts. We treat the problem by means of the stochastic Pontryagin maximum principle, that here is considered for a class of problems where in the state equation either the state or the control depend on the past. Moreover the control acts on the martingale term and the space of controls U can be chosen to be non-convex but now the space of controls U can be chosen to be non-convex. The maximum principle is thus formulated using a first-order adjoint Backward Stochastic Differential Equations (BSDEs), which can be explicitly computed due to the specific characteristics of the model, and a second-order adjoint relation.