Production of the doubly strange Ξ~- hyperon, known as a cascade particle, has been investigated in nuclear reactions in a wide energy range. However, only the results for the energies above the threshold for cascade production in elementary collisions were known for a long time. The first measurement of the subthreshold Ξ~- production was performed in heavy ion and nucleon-nucleus collisions by the HADES Collaboration. Because of the discrepancy between data and various model predictions deeper studies of the strangeness production, especially in elementary collisions near the threshold, are needed. In this paper simulations of the cascade production in proton-proton reaction at the beam kinetic energy of 4.5 GeV are presented. The results are relevant for the experiment planned by HADES with the upgraded setup during the FAIR-Phase 0 project.
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