A novel portfolio optimization method and its application to the hedging problem

In this article we will propose a novel, self-financing, dynamic and path dependent portfolio trading strategy which is based on the well known principle "sell high - buy low". Trading strategies are important also for the hedging problem selling/buying an option. The main problem of the writer of an option is how to invest the amount that she has received selling the option therefore the proposed trading strategy play an important role here. We will see that the hedging problem reduces to an optimization one and therefore the portfolio optimization and the hedging problem are closely related. We will also propose a deterministic portfolio selection method (i.e., without making any assumption-guess about the assets) and a notion of a deterministic fair price of an option.