Pricing conspicuous consumption products in recession periods with uncertain strength

Abstract

We compare different approaches of optimization under uncertainty in the context of pricing strategies for conspicuous consumption products in recession periods of uncertain duration and strength. We consider robust worst-case ideas and how the concepts of Value at Risk (VaR) and Conditional Value at Risk (CVaR) can be incorporated efficiently. The approaches are generic in the sense that they can be applied to other economic decision-making problems with uncertainty. We discuss the strengths and weaknesses of these approaches in general. We quantify runtimes and differences when applied to the special case of pricing decision making. We notice that VaR results in reliable strategies, although it is not a coherent measure of risk. The CVaR idea that has become the method of choice in financial mathematics is a very risk-averse version of safeguarding and thus a bit too conservative for pricing decisions. Also the resulting optimal control problem is the most expensive one from a computational point of view. From an economic point of view we observe different safeguarding strategies with respect to when and how prices are adapted. Qualitatively, no surprises arise: The more conservative a strategy is, the sooner prices are reduced to avoid bankruptcy. Yet, the discussion of the advantages and disadvantages is generic and can be transferred to other economic problems. The underlying mathematical model simplifies, as is often the case in economics. In the long run, there is a necessity to consider stochastic processes for the evolvement in time to reduce model-plant mismatch. Thus, our work to understand the behavior of the deterministic model and the impact of different robustification techniques should be seen as a step in this direction and as a blueprint for similar decision-making tasks with quantitatively verified mathematical models.