So your random variables $X$ and $Y$ have Gamma distributions with scale parameters $x_0$ and $y_0$ and shape parameters $1-\tau$ and $1-\kappa$ respectively (of course, you must assume $\tau < 1$ and $\kappa < 1$ for these to be well-defined). I presume you are also assuming $X$ and $Y$ are independent. Maple says the probability density function of $Z=XY$ is $$ \frac{2}{\Gamma(\tau) \Gamma(\kappa)} {z}^{{\tau/2}+{\kappa/2}-1}{y_{{0}}}^{-{\tau/2}-{\kappa/2}}{x_{{0}}}^{-{\tau/2}-{\kappa/2}} {{\rm K}_{\kappa-\tau}\left({\frac {2 \sqrt {z}}{\sqrt {x_{{0}}y_{{0}}}}}\right)} $$ where $K_{\kappa-\tau}$ is a modified Bessel function of the second kind.

So your random variables $X$ and $Y$ have Gamma distributions with scale parameters $x_0$ and $y_0$ and shape parameters $1-\tau$ and $1-\kappa$ respectively (of course, you must assume $\tau < 1$ and $\kappa < 1$ for these to be well-defined). I presume you are also assuming $X$ and $Y$ are independent. Maple says the probability density function of $Z=XY$ is $$ f_Z(z) = \frac{2}{\Gamma(\tau) \Gamma(\kappa)} {z}^{{\tau/2}+{\kappa/2}-1}{y_{{0}}}^{-{\tau/2}-{\kappa/2}}{x_{{0}}}^{-{\tau/2}-{\kappa/2}} {{\rm K}_{\kappa-\tau}\left({\frac {2 \sqrt {z}}{\sqrt {x_{{0}}y_{{0}}}}}\right)} $$ for $z > 0$, where $K_{\kappa-\tau}$ is a modified Bessel function of the second kind.