Applied Stochastic Models in Business and Industry

Srinivasan, Shuba; Bass, Frank M.

2000 Applied Stochastic Models in Business and Industry

doi: 10.1002/1526-4025(200007/09)16:3<159::AID-ASMB417>3.0.CO;2-R

The present study uses modern time series methodology to understand long‐run equilibrium in markets and provides additional evidence of the frequent existence of stationary market shares for frequently purchased consumer products. Dekimpe and Hanssens, Marketing Science 1995; 14(2):G109–121 using a database of over 400 prior studies, found that 78 per cent of the market share series they studied were stationary, but that 68 per cent of the sales series were evolving. Our findings reconcile these results. A major contribution of this paper is its demonstration that the prior empirical evidence that a majority of sales series is in evolution is consistent with stationary market shares, if brand sales and category sales are cointegrated. To the extent that competitive activities have an effect on market share, an implication of our findings is that these activities may, in general, only have a temporary effect on market share. Finally, we distinguish, from a strategic perspective, between sales and share response at the primary‐demand level (category sales), selective‐demand level (brand sales) and relative‐position level (market share) and identify strategic scenarios depending upon their stable/evolving nature. Copyright © 2000 John Wiley & Sons, Ltd.

Chetouani, H.; Korolyuk, V. S.

2000 Applied Stochastic Models in Business and Industry

doi: 10.1002/1526-4025(200007/09)16:3<179::AID-ASMB421>3.0.CO;2-1

Stationary distribution of repairable systems with limited service and spare devices is considered on an equilibrium set by using the Gibbs potential representation. As an application we consider the reliability of k‐out‐of‐n system. Copyright © 2000 John Wiley & Sons, Ltd.

Karoui, Nicole El; Geman, Helyette; Lacoste, Vincent

2000 Applied Stochastic Models in Business and Industry

doi: 10.1002/1526-4025(200007/09)16:3<197::AID-ASMB414>3.0.CO;2-Q

This paper discusses the introduction and the selection of a finite set of state variable in arbitrage‐free models of the term structure of interest rates. We choose a Gaussian setting which offers, as it is well known, tractable computations, hence results easier to understand and interpret. We study the mathematical conditions under which interest rates can be taken as state variables and address the key issues of time homogeneity of the model for a given set of state variables and the role of the current yield curve. Lastly, we provide explicit empirical estimations for four different swap markets (France, Italy, Japan, United Kingdom) and show that the state variables extracted through the use of a Kalman filter approach can be identified with linear combinations of interest rates. Copyright © 2000 John Wiley & Sons, Ltd.

Bloch‐Mercier, Sophie

2000 Applied Stochastic Models in Business and Industry

doi: 10.1002/1526-4025(200007/09)16:3<219::AID-ASMB416>3.0.CO;2-4

We consider a reparable system with a finite state space, evolving in time according to a semi‐Markov process. The system is stopped for it to be preventively maintained at random times for a random duration. Our aim is to find the preventive maintenance policy that optimizes the stationary availability, whenever it exists. The computation of the stationary availability is based on the fact that the above maintained system evolves according to a semi‐regenerative process. As for the optimization, we observe on numerical examples that it is possible to limit the study to the maintenance actions that begin at deterministic times. We demonstrate this result in a particular case and we study the deterministic maintenance policies in that case. In particular, we show that, if the initial system has an increasing failure rate, the maintenance actions improve the stationary availability if and only if they are not too long on the average, compared to the repairs ( a bound for the mean duration of the maintenance actions is provided). On the contrary, if the initial system has a decreasing failure rate, the maintenance policy lowers the stationary availability. A few other cases are studied. Copyright © 2000 John Wiley & Sons, Ltd.