Calculations of the first and second ionization potentials and electron affinities of superheavy elements 115-117 are presented. The calculations are performed in the framework of the Dirac-Coulomb Hamiltonian, and the results are corrected for the Breit and QED contributions. Correlation is treated by the relativistic coupled cluster approach with single, double, and perturbative triple excitations [CCSD(T)]. The same approach is used to calculate the ionization potentials and electron affinities of the lighter homologues, Bi, Po, and At. Comparison of the available experimental values for these atoms, namely, the first ionization potentials (IPs) of Bi, Po, and At and the second IP and EA of Bi, with our results shows excellent agreement, within a few hundredths of an eV, lending credence to our predictions for their superheavy homologues. High-accuracy predictions are also made for the second ionization potentials and electron affinities of Po and At, where no experiment is available.