The Research On Applying Martingale Process To Option Pricing

In the text I mainly talk about the problem of applying martingale process to option pricing. Using the property of martingale process, I consider, when there being no transact cost, when there being proportional transact cost and when there being concave transact cost, European Option buying price and selling price respectively, and at the same time, give correspondent pricing formula. Furthermore, I also research on the problem of American Option pricing when there being no transact cost using the property of martingale process. And I give correspondent buying price, selling price and some conclusions.