Reset Put Option Pricing with Transaction Costs

In order to price some exotic options in the presence of transaction costs, the new type of reset option is considered. By incorporating the random stopping property of the American option, we propose some pricing theorems. The specific reset option pricing is within the framework of portfolio optimization problems. Utility functions are defined so as to derive the utility indifference prices for the reset option buyers. Detailed numerical procedures are proposed for computing reset option prices and the corresponding optimal trading strategies. We also elaborate on the practical procedures of implementing our numerical algorithms and some direction of the future work.