Catálogo de publicaciones - libros

This paper considers a specific marketing problem based on a model by Gould (1970). The extension is that we have two kinds of advertising directed towards new customers and existing customers, respectively. We found that history dependent behavior occurs: if initial goodwill is small then it does not pay to spend a lot of money on advertising towards existing customers. Consequently convergence to a saddle point with low goodwill prevails where there is only advertising with the aim to attract new customers. On the other hand, for larger initial goodwill, eventually a steady state with a high goodwill level is reached where both types of advertising are used.

Advertising budget allocation with carryover effects over time is a problem that was treated extensively by economists. Additional developments were carried out by Sethi who has also provided some outstanding review papers. The model treated by Sethi were essentially defined in terms of optimal control problems using deterministic advertising models while my own were essentially sales response stochastic models with advertising budget determined by stochastic control problems. These problems continue to be of academic and practical interest. Issues relating to the “advertising message” such as truthful claims advertising directed to first time buyers has not attracted much attention however.

The purpose of this paper is to address issues relating to advertising and their messages by suggesting a stochastic advertising-repeat purchase model. In this model, advertising directed to first time buyers is essentially defined by two factors: the advertising budget and the advertising message (such as statement regarding the characteristics of a product, its lifetime etc.). Consumers experience in case they buy the product will define the advertising message “reliability”, namely that the probability that advertised message are confirmed or not. Repeat purchasers, however, are influenced by two factors, on the one hand the advertising messages that are directed to experienced consumers and of course the effects of their own experience (where past advertising claims whether truthful, or not, interact with customers’ personal experience). Advertising claims that underestimate products characteristics might be “reliable” but then they might not entice first time purchasers, while overly optimistic advertising messages might entice first time purchasers but be perceived as unreliable by repeat purchasers who might switch to other competing brands. In this sense, the decision to advertise is necessarily appended by the decision to “what to advertise”, which may turn out to be far more important for a firm. This paper provides a theoretical approach to deal with this issue.

We study an optimal control problem with a man-made capital stock, and a stock of renewable natural resource. They are substitutable inputs in the production of the final good. Starting from low levels of both stocks, the optimal policy consists of three phases. In phase I, the planner builds up the stock of resource above its steady state level, while the man-made capital stock is kept below its steady state level. In phase II, the resource stock declines steadily, while the man-made capital stock continues to grow, until the steady state is reached, and the economy stays thereafter. The model exhibits “overshooting” property.

In this brief paper one shows the relevance of asymptotic control theory to the study of economic sustainable development. One also proposes a modeling framework where sustainable economic development is represented through a paradigm of optimal stochastic control with two time-scales. This shows that several contributions of Prof. Sethi, in the domain of hierarchical and multi-level control models in manufacturing and resource management can also serve to better understand the stakes of sustainability in economic growth and to assess long term environmental policies.

We present a model of exploitation of a common property resource when agents can also invest in private and productive capital. The resource extracted from a common pool is non-renewable, but the resource stock is under uncertainty in the sense that the stock might follow jump process. We show that there exists an optimal solution in the model.

In this paper our concern is with deforestation as a global environmental issue. Foreign transfers from developed countries to forestry countries have been proposed for this goal. The problem is formulated as a Stackelberg differential game played over an infinite horizon, with the donor community as the leader and the aid recipient country as the follower. We consider different transfer mechanisms through which the donor community subsidizes the forestry country. We compare the results both from the environmental and economic points of view.

We derive irrigation management schemes accounting for the dynamic response of biomass yield to salinity and soil moisture as well as for the cost of irrigation water. The simple turnpike structure of the optimal policy is characterized using Green’s Theorem. The analysis applies to systems of arbitrary end conditions. A numerical application of the turnpike solution to sunflower growth under arid conditions reveals that by selecting the proper mix of fresh and saline water for irrigation, significant savings on the use of freshwater can be achieved with negligible loss of income.

Traditional approaches to forecast option prices and implement trading strategies make use of implied volatilities. Noh, Engle, and Kane (1994) propose a different approach. Based on conditional variance models of the GARCH type they forecast volatility and use these forecasts to predict future option prices. In combination with simple trading rules Noh et al. evaluate the profitability of these forecasts for the S&P 500 index. In this paper we take up their approach and apply it to Bund future options. We show that volatility forecasts together with simple option trading strategies create value. The profits can be significant even when transaction costs are taken into account.

A two-part tariff is a non-linear pricing technique in which the price of a product or service is composed of two parts: an entrance fee and a charge per unit of consumption. Compared to linear pricing, this methodology leads to higher profits by allowing a firm more freedom in extracting the consumer surplus. It is widely used in telecommunication services.

This chapter documents recent developments on non-linear pricing in a dynamic and competitive environment. The developments can also be viewed as extensions of the linear dynamic pricing literature by allowing a two-part tariff scheme.

The paper is about pension fund problems where an agent pays an amount to the fund manager and is repaid, after time , a lump sum (). Such problems admit an analytical solution for specific, rather unrealistic formulations. Several practical pension fund problems are converted in the paper into Markov decision chains solvable through approximations. In particular, a couple of problems with a non-differentiable asymmetric (with respect to risk) utility function are solved, for which left-skewed fund-return distributions are reported. Such distributions ascribe more probability to higher payoffs than the right-skewed ones that are common among analytical solutions.