Research On The Price Of The Geometric Average Asian Options With A Jump

The main purpose of this article is to solve Asian option in a jump-diffusion model in financial mathematics. In the Black-Scholes models, The stock price is driven by the Brown motion. It is a continuous function of time. But some important events can lead to brusque variations in price. To model this kind of phenomena, we have to introduce discontinuouse stochastic process.Under the assumption that the stock price is Black-Scholes with a jump ,which is baseed upon resolvent of the Markov processes and Laplace transform, so we can obtain a closed-form solution to the call Asian option with geometric average assets prices in a continuouse situation, so too the put Asian option with the connections between with them .