This work analyzes lognormal diffusion processes with a multisigmoidal logistic mean, subject to random catastrophic events. The occurrence of such catastrophes is governed by a counting process N(t), and upon each catastrophic event, the process restarts from a random state. The resulting process is employed as a model to describe phenomena of an economic and financial nature. In particular, we conduct a simulation study in which the process replicates the dynamics of bank capital, with catastrophes governed by a Poisson process and restart points fixed at the bailout level. Furthermore, we propose an application to real data related to Industrial Production Index (IPI) in which the time arrivals of the catastrophes are fixed and the restart points are binomially distributed. Such application confirms the relevance of the proposed model.