The article solves three different optimal stopping problems related to stock options using the Black-Scholes model. It addresses perpetual lookback American options, new stock options with guaranteed minimums, and call options for risk-averse buyers. The researchers found that the free boundary for the perpetual lookback American option is governed by a nonlinear ordinary differential equation, the value of the new stock option is determined by solving a nonalgebraic equation, and the optimal policy for the call option depends on the ratio of the current stock price to a fixed constant chosen by the buyer.