This article presents a dynamic pricing model of a retailer selling an inventory, accounting for consumer behavior. The authors propose an optimal control model, maximizing the intertemporal profit with consumers sensitive to the selling price and to a reference price. The optimal dynamic...

This paper presents a review of recent developments that have taken place in the area of dynamic optimal control models in advertising subsequent to the comprehensive survey of the literature by Sethi in 1977. The basic problem underlying these models is that of determining optimal advertising...

This article presents a dynamic pricing model of a retailer selling an inventory, accounting for consumer behavior. The authors propose an optimal control model, maximizing the intertemporal profit with consumers sensitive to the selling price and to a reference price. The optimal dynamic...

We examine an oligopoly model of advertising competition where each firm's market share depends on its own and its competitors' advertising decisions. A differential game model is developed and used to derive the closed-loop Nash equilibrium under symmetric as well as asymmetric competition. We...

This note extends the finding of Benhabib and Rusticchini (1994) who provide a class of SDGE models, whose solution is characterized by a constant savings rate. We show that this class of models may be interpreted as a standard representative agent SDGE model with costly adjustment of capital...

In this paper I give a method for finding long-run-average policies in the undiscounted economic growth problem using approximations by finite horizons. Required hypothesis is the strong interiority of T-horizon solutions.

This paper explores sufficient conditions for a continuous stationary Markov optimal policy and a concave value function in stochastic dynamic programming problems. Also, the paper addresses conditions needed for the differentiability of the value function. The paper uses conditions such as...

Finding solutions to the Bellman equation often relies on restrictive boundedness assumptions. In this paper we develop a method of proof that allows to dispense with the assumption that returns are bounded from above. In applications our assumptions only imply that long run average (expected)...

This note studies a general nonstationary infinite-horizon optimization problem in discrete time. We allow the state space in each period to be an arbitrary set, and the return function in each period to be unbounded. We do not require discounting, and do not require the constraint...

These notes provide an intuitive introduction to dynamic programming. The first two Sections present the standard deterministic Ramsey model using the Lagrangian approach. These can be skipped by whom is already acquainted with this framework. Section 3 shows how to solve the well understood...