<p>An Asian extremum option is a path-dependent multi-asset option whose payoff depends on the extremum value (either minimum or maximum) of average prices (either arithmetic or geometric) of several underlying variables over a given period. In this paper, we derive pricing closed-from solutions for geometric Asian extremum options on maximum or minimum of two assets under the correlated two-asset mixed fractional Brownian motion with jumps (JMFBM). We also present useful formulas for Deltas as well as the Gammas and Cross-Gamma of geometric Asian call option on the maximum. Numerical examples are provided to analyze the impacts of model parameters on option price and its Greeks. In addition, we verify that our closed-form solution has been accurately and efficiently obtained by comparing those with the Monte Carlo simulation method. For better understanding, we provide a numerical result to compare the option price given by different models. This result shows that our adopted model is more consist with the real market.</p>