Optimal Advertizing Policy for Selling a Single Asset

Abstract

Suppose we have a single asset that we would like to sell. As time goes by, independent and identically distributed offers with a common known distribution F are given to us. At any given moment, we may either accept the current offer or reject it, thereby losing it forever. The rate at which offers arrive follows a nonhomogeneous Poisson process whose instantaneous intensity is under our control, using advertizing in a manner to be described. Our objective is, roughly, that of maximizing the total discounted expected reward composed of the offer we decide to accept, minus the total advertizing costs.