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Asian Perpetuities
 Svoboda, Miroslav ; Večeř, Jan (advisor) ; Čoupek, Petr (referee)
This Master thesis studies the Asian perpetuity, which is the European type option with the average asset as the underlying asset and the execution time of the option in infinity. Assuming the geometric Brownian motion model of an asset, the thesis studies the behavior of the average of the asset. Three different types of averaging are considered: arithmetic, geometric and harmonic average. The average values of the log-normals maintain the known distribution only for the geometric average but, as it is shown in the thesis, when the average is examined on infinite time horizon, the arithmetic and harmonic averages maintain the inverse gamma distribution or gamma distribution, respectively. This result enables the computation of the price of Asian perpetuity which is also examined in the thesis. 1
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