A variety of continuous-time differential functions have been developed to investigate
dynamic advertising problems in business and economics fields. Since major dynamic …

The main objective of this book is to give an overview of the theory of Hamilton–Jacobi–
Bellman (HJB) partial differential equations (PDEs) in infinite-dimensional Hilbert spaces …

We study the problem of adaptive control of a high dimensional linear quadratic (LQ) system.
Previous work established the asymptotic convergence to an optimal controller for various …

This paper proposes a tool to control cooperative advertising which increases the goodwill
of companies operating in a competitive market. We introduce the lag between advertising …

Optimal control theory is a branch of mathematics developed to find optimal ways to control
a dynamic system. Thus the theory applies to many management science and economics …

We consider a pricing and advertising dynamic-optimization problem where the goodwill
dynamics evolve à la Nerlove–Arrow. The firm maximizes its profit over a finite-planning …

The problem of a firm willing to optimally promote and sell a single product on the market is
here undertaken. The awareness of such product is modeled by means of a Nerlove–Arrow …

Firms in the US spend over $200 billion each year advertising their products to consumers,
around one percent of the country's gross domestic product. It is of great interest to …

Consider the problem of learning the drift coefficient of a p-dimensional stochastic
differential equation from a sample path of length T. We assume that the drift is parametrized …

Segmentation is a core strategy in modern marketing, and age-specific segmentation based
on the age of the consumers is very common in practice. Age-specific segmentation enables …