Stochastically optimal advertising policies under dynamic conditions: The ratio rule

Kalyan Raman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


There has been considerable debate among marketing researchers about the optimality of popularly used advertising policies. In particular, the ratio rule has aroused much interest. This paper analyses its optimality under the expected profit maximization criterion for a general class of models. The optimality of the ratio rule extends to the stochastic case provided that the conditions which ensure its optimality for the deterministic case are enlarged by an additional restriction. This additional restriction has the effect of transforming the stochastic evolution of goodwill and sales to log‐normal processes. Advertising dynamics, the nature of the response function and unexplained error variance all interact to determine whether the ratio rule is exactly optimal, approximately optimal or not optimal at all.

Original languageEnglish (US)
Pages (from-to)283-288
Number of pages6
JournalOptimal Control Applications and Methods
Issue number3
StatePublished - 1990


  • Advertising‐sales models
  • Optimal advertising
  • Ratio rule
  • Stochastic optimal control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Control and Optimization
  • Applied Mathematics


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