In this paper, we study the problem of pricing average strike options in the case where the price processes are jump diffusion processes. As to the striking value we take the geometric average of the price process. Two cases are studied in details: One is the case where the jumping law of the...

The Langevin equation derived by Shibata and Hashitsume with the help of the projection operator formula is shown to be the stochastic differential equation of the Ito type. From their derivation, it is natural to interpret it as that of the Stratonovich type. However, comparing the...

In financial markets traders often protect their position from a significant decline by using a trailing stop. Assume the trader is long the market (owns the security). A trailing stop is an order to sell the security at the market, if the price of the security drops to the stop price. The stop...