Aims. We analyze the jovian Trojan dust in the L 4 swarm. Methods. To do this, we use a modification of the numerical code developed by us and previously applied to the collisional and dynamical evolution of the L 4 jovian Trojans. This algorithm considers catastrophic collisions and cratering events, includes a dynamical treatment that takes the stability and instability zones of the L 4 jovian swarm into account, and incorporates the effects of the Poynting-Robertson radiation.Results. From this analysis, we infer that the time evolution of the L 4 jovian Trojan dust luminosity has the characteristics of a diffusion process, since its current value is fairly insensitive to variations in the initial size distribution. Moreover, our results indicate that the current luminosity of the dust in the L 4 jovian swarm ranges from ∼3.2 × 10 −8 to 3.4 × 10 −8 L . Conclusions. From these estimates, we conclude that the current luminosity of the dust in the L 4 jovian swarm is comparable to the luminosity of the inner Solar System dust, and, at least, one order of magnitude lower than the luminosity of the outer Solar System dust.