We have studied the photoluminescence spectra of ${\mathrm{In}}_{\mathit{y}}$${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$As self-assembled quantum dots in ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As matrices with magnetic fields up to B=40 T. The quantum dot structure is pseudomorphically grown by molecular-beam epitaxy on (100) GaAs substrates. From the analysis of the diamagnetic shift of the magnetoluminescence spectra, we estimate the total lateral electron and hole confinement energy to be 43 meV. The exciton radius is deduced as 5 nm. The exciton binding energy in such a quantum dot system is estimated to be \ensuremath{\sim}31 meV based on trial wave-function calculations of the actual dot system. \textcopyright{} 1996 The American Physical Society.