I study a dynamic pricing problem in which a seller with limited inventory must sequentially price a perishable product for arriving customers with heterogeneous valuations. The key difficulty lies in balancing immediate sales against future opportunities under capacity constraints and stochastic customer valuations. I propose a simple, interpretable, and asymptotically optimal dynamic pricing algorithm, called Dynamic Run-Out Pricing (DROP), that adjusts prices in real time based on current inventory and anticipated future demand. Under the assumption that customers' valuations follow bounded or exponential distributions, our theoretical results show that DROP's expected revenue converges to the optimal revenue as market size grows. Unlike traditional notions of near-optimality, where the ratio of the algorithm's revenue to the optimal revenue converges to 1, I show that the absolute difference between the two revenues converges to 0 as the market size increases, underscoring the algorithm's effectiveness. Furthermore, I extend our analysis to heavy-tailed valuation distributions, specifically the Pareto distribution, where standard run-out heuristics severely underprice inventory by ignoring the value of waiting for extreme valuations. To correct this, I introduce the Tail-Aware DROP (TA-DROP) heuristic, which intentionally inflates prices to protect inventory, and I prove that it restores asymptotic optimality with a strict polynomial convergence rate.

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