We obtain closed-form expressions for the value of the joint Laplace transform of the running maximum and minimum of a diffusion-type process stopped at the first time at which the associated drawdown or drawup process hits a constant level before an independent exponential random time. It is...

We obtain closed-form expressions for the value of the joint Laplace transform of the running maximum and minimum of a diffusion-type process stopped at the first time at which the associated drawdown or drawup process hits a constant level before an independent exponential random time. It is...

We present explicit solutions to the perpetual American compound option pricing problems in the Black-Merton-Scholes model. The method of proof is based on the reduction of the initial two-step optimal stopping problems for the underlying geometric Brownian motion to appropriate sequences of...

We derive closed form solutions to the discounted optimal stopping problems related to the pricing of the perpetual American standard put and call options in a diffusion model with piecewise-linear coefficients. The method of proof is based on the reduction of the initial optimal stopping...

We study the perpetual American call option pricing problem in a model of a financial market in which the firm issuing a traded asset can regulate the dividend rate by switching it between two constant values. The firm dividend policy is unknown for small investors, who can only observe the...