We analyze the optimal sales process of a stochastic advertising and pricing model with constant demand elasticities. We derive explicit formulae of the densities of the (optimal) sales times and (optimal) prices when a fixed finite number of units of a product are to be sold during a finite sales period or an infinite one. Furthermore, for any time t the exact distribution of the inventory, i.e. the number of unsold items, at t is determined and will be expressed in terms of elementary functions. Approximations of the densities of sales times by particular beta densities are proposed. Results related to the infinite horizon model are by-products of the finite horizon analysis.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc105-0-9,
author = {Kurt L. Helmes and Torsten Templin},
title = {Explicit formulae of distributions and densities of characteristics of a dynamic advertising and pricing model},
journal = {Banach Center Publications},
volume = {104},
year = {2015},
pages = {119-142},
zbl = {1334.60186},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc105-0-9}
}
Kurt L. Helmes; Torsten Templin. Explicit formulae of distributions and densities of characteristics of a dynamic advertising and pricing model. Banach Center Publications, Tome 104 (2015) pp. 119-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc105-0-9/