Discounted Optimal Stopping Problems for Maxima of Geometric Brownian Motions With Switching Payoffs

Abstract We present closed-form solutions to some discounted optimal stopping problems for the running maximum of a geometric Brownian motion with payoffs switching according dynamics continuous-time Markov chain two states. The proof is based on reduction original equivalent free-boundary and solution latter by means smooth-fit normal-reflection conditions. show that boundaries are determined as maximal associated two-dimensional systems first-order nonlinear ordinary differential equations. obtained results related valuation real lookback options fixed floating sunk costs in Black–Merton–Scholes model.