On sales effort and pricing decisions under alternative risk criteria

In the literature, different risk criteria are proposed for risk-averse decision-making, but it is often unclear which risk criteria should be used and what their differences may be. This study investigates this problem when a risk-averse, make-to-order firm decides its pricing and sales effort, two factors affecting demand. We consider alternative risk criteria commonly used in the literature, namely expected utility theory (EUT), mean-variance (MV), mean-semideviation (MS), value-at-risk (VaR), conditional value-at-risk (CVaR), and loss aversion (LA). We find that all of these criteria lead to similar qualitative behaviors regarding how risk-/loss-averse decisions deviate from risk-neutral ones. A particularly interesting result is that the form of demand randomness, i.e., additive or multiplicative, can completely reverse the effect of risk/loss aversion in certain cases. We also find that the risk aversion models, i.e., EUT, MV, MS, VaR, and CVaR, are essentially equivalent in inducing the same set of optimal solutions under adverse market states. However, loss aversion is a mild version of risk aversion in that the LA model can only lead to a subset of the solutions generated by other models. These results may not be valid for other applications, such as the newsvendor pricing problem, so we can conclude that the relationship between alternative risk criteria is case-sensitive and should be evaluated more carefully.