This paper considers an optimal control problem with two state variables for the dynamics of the Nerlove-Arrow advertising model. The optimal control is the rate of advertising expenditure required to maximize the present value of net profit streams over an infinite horizon subject to a...

We consider a market consisting of two populations, termed rich and poor for convenience. If a product is priced such that it is very expensive for the poor, but affordable to the rich, then it becomes a status symbol for the poor and this makes it more desirable for the poor. At a lower price,...

Cooperative advertising is a key incentive offered by a manufacturer to influence retailers' promotional decisions. We study cooperative advertising in a dynamic retail duopoly where a manufacturer sells his product through two competing retailers. We model the problem as a Stackelberg...

Cooperative advertising is an important mechanism used by manufacturers to influence retailers' promotional decisions. In a typical arrangement, the manufacturer agrees to reimburse a fraction of a retailer's advertising cost, known as the subsidy rate. We consider a case of new product adoption...

We investigate firms' re-manufacturing strategies in the case of a Cournot duopoly. On one hand, re-manufactured products cannibalize sales of new products by the same firm and hurt its profits. On the other, re-manufacturing can be a profitable marketing strategy to target different customer...

The concept of a forecast horizon for a given player with respect to the set of equilibria in an abstract dynamic game is defined. Consideration is then given to the case of a stochastic dynamic game with memory-less perfect state information and the Nash equilibrium concept. Sufficient...

This note clarifies some issues dealing with the necessary condition for the optimal terminal time in free terminal time optimal control problems. It is shown that this condition is independent of the other maximum principle conditions and a simple proof is presented. Also the economic...

We consider two control problems on a finite horizon; one stochastic and the other deterministic. In both problems the running cost and the terminal cost are the same. The controllable input in both problems is of an additive nature with cost proportional to the input (which can be both positive...

The method of variational inequalities is a useful theoretical tool in stochastic control, but there are few problems in which this method leads to an explicit solution. We present such a problem drawn from portfolio management. An agent can distribute his wealth between two investments, one...

In this paper we analyse a control‐theoretic model of a country possessing a finite amount of a non‐renewable resource. The country can both consume the indigenous resource and export it. Moreover, a substitute for the indigenous resource is available at a given backstop price. We obtain the...