Pricing for European Weighted Geometric Average Value Asian Option

Based on the theory of Asian option valuation, we established a model for underlying asset price with a mixed diffusion process involving source of jump. Continuous component is modeled as geometric Brown motion to characterize its ``normal'' revolution and discontinuous component is modeled as jump with a Poisson process in conjunction with random jump size, and jump size has a log-normal distribution. By applying It\^o-Skorohod formula and equivalent martingale measure transformation within the framework of our model, we derived a closed form analytic solution for European weighted geometric average value Asian option, in addition to that, some other general forms are discussed.