Explicit formulae of distributions and densities of characteristics of a dynamic advertising and pricing model
Volume 105 / 2015
Banach Center Publications 105 (2015), 119-142
MSC: Primary 60K10, 60K30; Secondary 91B24, 91B70.
DOI: 10.4064/bc105-0-9
Abstract
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.
