Computational pricing for a special type of reset option with proportional transaction costs

In order to solve the special type of reset option in the presence of transaction costs, we adopt the Markov chain method as well as the dual analysis. By introducing mixed stopping times, gradient restriction and approximate martingales, we set up the framework to perform the algorithm for the special type of reset option. After that, we elaborate on the procedures for the reset option pricing in the presence of proportional transaction costs. Finally, we propose the reset option prices for the sellers and buyers and do some case analysis.