Theoretical analysis of the electron energy spectrum and the magnetization in a strained In<sub><i>x</i></sub>Ga<sub>1-<i>x</i></sub>As/GaAs selfassembled
quantum ring (SAQR) is performed using realistic parameters, determined from the cross-sectional
scanning-tunneling microscopy characterization. The Aharonov-Bohm oscillations in the persistent current have
been observed in low temperature magnetization measurements on these SAQRs. The effect of the Coulomb
interaction on the energy spectra of SAQRs is studied for rings with two electrons and with an exciton. Our
analysis of the photoluminescence spectrum in magnetic fields up to 30 T shows that the excitonic properties
strongly depend on the anisotropic shape, size, composition and strain of the SAQRs and is in a good agreement
with the experimental data.