  Price determination is a central research topic of revenue management in
marketing. The important aspect in pricing is controlling the stochastic
behavior of demand, and the previous studies have tackled price optimization
problems with uncertainties. However, many of those studies assumed that
uncertainties are independent of decision variables (i.e., prices) and did not
consider situations where demand uncertainty depends on price. Although some
price optimization studies have dealt with decision-dependent uncertainty, they
make application-specific assumptions in order to obtain an optimal solution or
an approximation solution. To handle a wider range of applications with
decision-dependent uncertainty, we propose a general non-convex stochastic
optimization formulation. This approach aims to maximize the expectation of a
revenue function with respect to a random variable representing demand under a
decision-dependent distribution. We derived an unbiased stochastic gradient
estimator by using a well-tuned variance reduction parameter and used it for a
projected stochastic gradient descent method to find a stationary point of our
problem. We conducted synthetic experiments and simulation experiments with
real data on a retail service application. The results show that the proposed
method outputs solutions with higher total revenues than baselines.
