Numerical computation for Bermuda reset option with proportional transaction costs

In order to solve the Bermuda reset option in the presence of transaction costs, the Markov chain and dual analysis are adopted in the pricing procedures. By introducing mixed stopping times, gradient restriction and domain restriction, we construct the framework which is essential for us to perform the algorithm. After the basic setups, we elaborate on the procedures for the reset option pricing in the presence of transaction costs. By using the dual analysis, we finally propose the reset option prices for the sellers and buyers.