Uncertain demand in pricing problems is often modeled using the sum of a linear price-response function and a zero-mean random variable. In this paper, we argue that the presence of uncertainty motivates the introduction of nonlinearities in the demand as a function of price, both in the risk-neutral and risk-sensitive models. We motivate our analysis by investigating the impact of uncertainty on the individual customers' valuations. We derive a family of price response functions, parametrized by a risk sensitivity coefficient, which includes the special case of risk neutrality.
Technical Report, Lehigh University, Dept of Industrial and Systems Engineering, Bethlehem, PA 18015, USA.