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The mixed fractional Brownian motion ($mfBm$) has become quite popular infinance, since it allows one to model long-range dependence and self-similaritywhile remaining, for certain values of the Hurst parameter, arbitrage-free. Inthe present paper, we propose approximate closed-form solutions for pricingarithmetic Asian options on an underlying described by the $mfBm$.Specifically, we consider both arithmetic Asian options and arithmetic Asianpower options, and we obtain analytical formulas for pricing them based on aconvenient approximation of the strike price. Both the standard $mfBm$ and the$mfBm$ with Poisson log-normally distributed jumps are taken into account.

Actuarial strategy for pricing Asian options under a mixed fractional Brownian motion with jumps