On the Modelling of Price Effects in the Diffusion of Optional Contingent Products

In this chapter, we study the pricing strategies of firms in a multi-product diffusion model where we use a new formalization of the price effects. More particularly, we introduce the impact of prices on one of the factors that affect the diffusion of new products: the innovation coefficient. By doing so, we relax one of the hypotheses in the existing literature stating that this rate is constant. In order to assess the impact of this functional form on the pricing policies of firms selling optional contingent products, we use our model to study two scenarios already investigated in the multiplicative form model suggested by Mahajan and Muller (1991) (M&M). We follow a ‘logical experimentation’ perspective by computing and com- paring the results of three models: (i) The M&M model, (ii) a modified version of M&M where the planning horizon is infinite, and (iii) our model, where the new formalization of the innovation effect is introduced. This perspective allows us to attribute the differences in results to either the length of the planning horizon, or to our model’s formalization. Besides its contribution to the literature on pricing and diffusion, this paper highlights the sensitiv- ity of results to the hypothesis used in product diffusion modelling and could explain the mixed results obtained in the empirical validations of diffusion models (Mesak, 1996).MINECO under projects ECO2014-52343-P and ECO2017-82227-P (AEI) and by Junta de Castilla y León VA024P17 and VA105G18 co-financed by FEDER funds (EU)

An examination of the interfaces between operations and advertising strategies

This dissertation is composed of three journals examining the interfaces between the marketing variable of advertising and various aspects of the operations function of the enterprise, namely, (1) production cost [Chapter 2], (2) inventory control [Chapter 3], and (3) service cost learning [Chapter 4]. The first journal identified the optimum advertising allocation policy over time in the presence of a quadratic convex/concave production cost function when the advertising response function is concave using a modified Vidale-Wolfe model. Through analytical proofs and numerical simulations, the results indicated the potential superiority of a pulsation policy in the presence of concavity in the advertising response function only if the production cost function is convex; otherwise, the uniform policy would be optimal. The study is seen as applicable to frequently purchased products in the maturity stage of their life cycles of dominant firms in their industries practicing a zero-inventory policy in a just-in-time environment. The research objective pertaining to the second journal was to study how a firm would adapt optimum ordered quantity/production lot size and optimum advertising expenditure in response to changes in its own parameters, rival\u27s parameters, or parameters that are common to all firms in a symmetric duopoly/oligopoly market. This was accomplished by developing comparative statics (sensitivity analysis) of a symmetric competitive inventory model with advertising-dependent demand based on a market share attraction model. Both optimum advertising expenditure and ordered quantity were found to be sensitive to changes in marketing and operations parameters. The robustness of the symmetric comparative statics was assessed by using data from the brewing industry in the US that represents an asymmetric oligopoly. The empirical analysis indicated that the theoretical results obtained for a symmetric oligopoly remained valid for an oligopoly where each firm had a market share less than 50% and the market shares were further apart from one another. The study is thought to be applicable to low-priced frequently purchased consumer items in competitive mature markets. In the third journal, the original Bass model for new products was modified to incorporate advertising and customers\u27 disadoption to characterize the optimum advertising policy over time for subscriber service innovations where service cost follows a learning curve. After characterizing the optimal policy for a general diffusion model, the results pertaining to a specific diffusion model for which advertising affects the coefficient of innovation were reported. On the empirical side, four alternative diffusion models were estimated and their predictive powers, using a one-step-ahead forecasting procedure, were compared. Empirical research findings suggest that the specific diffusion model considered in this study is not only of theoretical appeal, but also of notable empirical relevance. Taken together, the analytical and empirical findings argue in favor of advertising more heavily during the early stage of the diffusion process of the new subscriber service innovation and including a related message that would predominantly target innovators. Furthermore, it might be inappropriate to model the diffusion of subscriber services as if they were durable goods. The study is thought to be applicable to service innovations that are made available to customers periodically at a subscription fee. Typical examples include, but are not limited to, cable TV, health clubs, pest control, and the internet

Optimal Dynamic Procurement Policies for a Storable Commodity with L\'evy Prices and Convex Holding Costs

In this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at a random time by maximizing total expected profits. We model the firm's optimal procurement problem as a singular stochastic control problem in which controls are nondecreasing processes and represent the cumulative investment made by the firm in the spot market (a so-called stochastic "monotone follower problem"). We assume a general exponential L\'evy process for the commodity's spot price, rather than the commonly used geometric Brownian motion, and general convex holding costs. We obtain necessary and sufficient first order conditions for optimality and we provide the optimal procurement policy in terms of a "base inventory" process; that is, a minimal time-dependent desirable inventory level that the firm's manager must reach at any time. In particular, in the case of linear holding costs and exponentially distributed demand, we are also able to obtain the explicit analytic form of the optimal policy and a probabilistic representation of the optimal revenue. The paper is completed by some computer drawings of the optimal inventory when spot prices are given by a geometric Brownian motion and by an exponential jump-diffusion process. In the first case we also make a numerical comparison between the value function and the revenue associated to the classical static "newsvendor" strategy.Comment: 28 pages, 3 figures; improved presentation, added new results and section

Introduction of Software Products and Services Through Public 'Beta' Launches

Public 'Beta' launches have become a preferred route of entry into the markets for new software products and web site based services. While beta testing of novel products is nothing new, typically such tests were done by experts within firm boundaries. What makes public beta testing so attractive to firms? By introducing semi-completed products in the market, the firm can target the early adopter population, who can then build the potential market through the word of mouth effect by the time the actual version of the product is launched. In addition, the information gathered through the usage of the public beta gives significant insights into customer preferences and consequently helps in building a better product. We build these marketing and product development implications in an analytical model to compare the different product introduction strategies like 'skimming' or 'penetration pricing' with beta launches. This analysis is done for products of branded and unbranded Web 2.0 companies like Google and Flickr etc. We also examine the impact of different monetization models like direct pricing and advertising on the beta launch strategy

Optimal monopoly investment and capacity utilization under random demand

Unique value-maximizing programs of irreversible capacity investment and capacity utilization are described and shown to exist under general conditions for monopolist exhibiting capital adjustment costs and serving random consumer demand for a nondurable good over an infinite horizon. Stationary properties of these programs are then fully characterized under the assumption of serially independent demand disturbances. Optimal monopoly behavior in this case includes acquisition of a constant and positive level of capacity, the maintenance of a positive expected value of excess capacity in each period, and an asymmetrical response of price to unanticipated fluctuations in consumer demand. Under a general form of Markovian demand, the effect of uncertainty on irreversible capacity investment is also described in terms of the discounted flow of expected revenue accruing to the marginal unit of existing capacity and the option value of deferring the acquisition of additional capital. The option value of deferring such acquisition, created by the irreversibility of capacity investment, is characterized directly in terms of the value function of the firm, and is then shown to be zero in a stationary equilibrium with serially independent demand disturbances. The response of investment to increase demand uncertainty depends, as a result, directly on the properties of the marginal revenue product of capital. A non-negative response of optimal capacity to increased uncertainty in market demand is demonstrated for a general class of aggregate consumer preferences.Industrial capacity

From (Martingale) Schrodinger bridges to a new class of Stochastic Volatility Models

Following closely the construction of the Schrodinger bridge, we build a new class of Stochastic Volatility Models exactly calibrated to market instruments such as for example Vanillas, options on realized variance or VIX options. These models differ strongly from the well-known local stochastic volatility models, in particular the instantaneous volatility-of-volatility of the associated naked SVMs is not modified, once calibrated to market instruments. They can be interpreted as a martingale version of the Schrodinger bridge. The numerical calibration is performed using a dynamic-like version of the Sinkhorn algorithm. We finally highlight a striking relation with Dyson non-colliding Brownian motions