Mathematical Models of Oversupply Risk in the Coastal Upscale Hotel Market of Vietnam: Entry Timing, Construction Lags and an Early Warning Index

Coastal resort cities in Vietnam have added upscale hotel rooms at a pace that repeatedly outruns demand. The usual explanation, developer optimism, sits awkwardly beside the fact that most of these projects are appraised with conventional discounted cash flow methods and financed by institutions with a strong incentive to avoid loss. This paper develops a mathematical framework in which oversupply emerges as a property of the market rather than as a failure of individual judgement. Three blocks are combined: a delayed stock-and-flow accounting of rooms in preparation, under construction and in operation; a real options trigger governing when the marginal developer starts building; and a composite oversupply risk index that summarises the occupancy gap, the forward absorption time of the pipeline and the distance between asset value and replacement cost. The balanced growth path is derived analytically. We obtain a closed-form stability condition linking the construction lag to a critical feedback gain, and show that the cycle length at the stability boundary is 2(2τ + 1) years, so that a three-year lag falls inside the ten to fifteen year range reported for property cycles. Simulation under illustrative parameters indicates that competitive erosion of the option premium, rather than forecasting error, is the most powerful single driver of cycle severity, and that a cap on annual construction starts dominates both disclosure and lag reduction. The framework is specified so that it can be calibrated to one coastal city once room supply, pipeline and rate data are assembled.