Context. Exoplanet searches have revealed interesting correlations between the stellar properties and the occurrence rate of planets. In particular, different independent surveys have demonstrated that giant planets are preferentially found around metal-rich stars and that their fraction increases with the stellar mass. Aims. During the past six years we have conducted a radial velocity follow-up program of 166 giant stars to detect substellar companions and to characterize their orbital properties. Using this information, we aim to study the role of the stellar evolution in the orbital parameters of the companions and to unveil possible correlations between the stellar properties and the occurrence rate of giant planets. Methods. We took multi-epoch spectra using FEROS and CHIRON for all of our targets, from which we computed precision radial velocities and derived atmospheric and physical parameters. Additionally, velocities computed from UCLES spectra are presented here. By studying the periodic radial velocity signals, we detected the presence of several substellar companions. Results. We present four new planetary systems around the giant stars HIP 8541, HIP 74890, HIP 84056, and HIP 95124. Additionally, we study the correlation between the occurrence rate of giant planets with the stellar mass and metallicity of our targets. We find that giant planets are more frequent around metal-rich stars, reaching a peak in the detection of f = 16.7+15.5-5.9% around stars with [Fe/H] ~ 0.35 dex. Similarly, we observe a positive correlation of the planet occurrence rate with the stellar mass, between M∗ ~ 1.0 and 2.1 M⊙, with a maximum of f = 13.0+10.1-4.2% at M∗ = 2.1 M⊙. Conclusions. We conclude that giant planets are preferentially formed around metal-rich stars. In addition, we conclude that they are more efficiently formed around more massive stars, in the stellar mass range of ~1.0-2.1 M⊙. These observational results confirm previous findings for solar-type and post-MS hosting stars, and provide further support to the core-accretion formation model.