A dynamic theory of random price discounts

A seller with commitment power sets prices over time. Risk-averse buyers arrive to the market and decide when to purchase. We obtain that the optimal price path is a "regular" price, with occasional episodes of sequential discounts that occur at random times. The optimal price path has the property that the price a buyer ends up paying is independent of his arrival and purchase times, and only depends on his valuation. Our theory accommodates empirical findings on the timing of discounts.