Multiple Stopping Times and Exercise Boundaries for American Put Options

This quantitative finance paper focuses on finite-maturity American put options under a risk-neutral Black-Scholes model, with at most m exercise rights and a minimum interval δ > 0 between consecutive exercises. It proves that the number of remaining exercise rights corresponds to a unique exercise boundary, and that boundaries are ordered by the number of remaining rights. The paper also derives results including local Lipschitz continuity of exercise boundaries, smooth-fit properties, quasi-variational inequalities, and free-boundary formulations, and extends the recursive framework to independent random termination times.