# Explicit formulae of distributions and densities of characteristics of a dynamic advertising and pricing model

• Volume: 105, Issue: 1, page 119-142
• ISSN: 0137-6934

top

## Abstract

top
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.

## How to cite

top

Kurt L. Helmes, and Torsten Templin. "Explicit formulae of distributions and densities of characteristics of a dynamic advertising and pricing model." Banach Center Publications 105.1 (2015): 119-142. <http://eudml.org/doc/281633>.

@article{KurtL2015,
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.},
author = {Kurt L. Helmes, Torsten Templin},
journal = {Banach Center Publications},
keywords = {stochastic advertising-pricing model; optimal sales process; distributions; densities},
language = {eng},
number = {1},
pages = {119-142},
title = {Explicit formulae of distributions and densities of characteristics of a dynamic advertising and pricing model},
url = {http://eudml.org/doc/281633},
volume = {105},
year = {2015},
}

TY - JOUR
AU - Kurt L. Helmes
AU - Torsten Templin
TI - Explicit formulae of distributions and densities of characteristics of a dynamic advertising and pricing model
JO - Banach Center Publications
PY - 2015
VL - 105
IS - 1
SP - 119
EP - 142
AB - 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.
LA - eng
KW - stochastic advertising-pricing model; optimal sales process; distributions; densities
UR - http://eudml.org/doc/281633
ER -

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.