Delayed Black And Scholes Formulas Driven By Lévy Processes

In this article,we mainly consider the effect,of the past in the determination of the fair price of a option,and the stock price process is modelled by a stochastic differential delay equation driven by Lévy processes.We construct an delayed option pricing model based on Black and Scholes formula.The model can be shown as (?)In the above model,Standard Brownian motion is replaced by Lévy process.When both function g and initial process ? meet the conditions,we can prove that the model admits a pathwise unique solution S(t).Because the noise process has jumps of random sizes,such a.market is incomplete and there is not,a unique equivalent martingale measure.Then,A Follmer-Schweizcr minimum measure has boen established through the method of Chan in order to determine the parameters under the given conditions.After the unique equivalent martingale measure Q in the delayed market being established,which makes the discounted price process S(t)a martingale.We can define a Lévy process as follow (?)we will enlarge the delayed Lévy market with a.series of additional assets based on the above mentioned processes through the method of Nualart.Under the meeasure Q define(based on Z)the ith-power-jump processes Y(i)and their orthonormalized version T(i),we enlarge the market with what we will call the orthonormalized ith-power-jump assets.We will make use of the MRP establish a self-financing tame strategy,which is replicating the claim X.Finally,we show that the portfolio is self-financing and the price of contingent claim X at time t as follow (?)...