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The multi-strange baryon yields in Pb--Pb collisions have been shown toexhibit an enhancement relative to pp reactions. In this work, $\Xi$ and$\Omega$ production rates have been measured with the ALICE experiment as afunction of transverse momentum, ${p_{\rm T}}$, in p-Pb collisions at acentre-of-mass energy of ${\sqrt{s_{\rm NN}}}$ = 5.02 TeV. The results coverthe kinematic ranges 0.6 GeV/$c<{p_{\rm T}} <$7.2 GeV/$c$ and 0.8GeV/$c<{p_{\rm T}}<$ 5 GeV/$c$, for $\Xi$ and $\Omega$ respectively, in thecommon rapidity interval -0.5 $<{y_{\rm CMS}}<$ 0. Multi-strange baryons havebeen identified by reconstructing their weak decays into charged particles. The${p_{\rm T}}$ spectra are analysed as a function of event charged-particlemultiplicity, which in p-Pb collisions ranges over one order of magnitude andlies between those observed in pp and Pb-Pb collisions. The measured ${p_{\rmT}}$ distributions are compared to the expectations from a Blast-Wave model.The parameters which describe the production of lighter hadron species alsodescribe the hyperon spectra in high multiplicity p-Pb. The yield of hyperonsrelative to charged pions is studied and compared with results from pp andPb-Pb collisions. A statistical model is employed, which describes the changein the ratios with volume using a canonical suppression mechanism, in which thesmall volume causes a species-dependent relative reduction of hadronproduction. The calculations, in which the magnitude of the effect depends onthe strangeness content, show good qualitative agreement with the data.

Multi-strange baryon production in p-Pb collisions at $\sqrt{s_\mathbf{NN}}=5.02$ TeV