Kurzbeschreibung: Classic Aalen–Johansen estimation targets transition probabilities in multi-state Markov models subject to for instance right-censoring. In particular, it belongs to the standard toolkit of health and disability insurance analytics. Following a brief introduction to actuarial multi-state modeling, we introduce the conditional Aalen–Johansen estimator, an innovative kernel-based estimator that allows for the inclusion of covariates and, importantly, is also applicable in non-Markov models. We establish uniform strong consistency and asymptotic normality under very lax regularity conditions; here, the theory of empirical processes plays a central role and leads to a transparent treatment. We also illustrate the practical implications and potential of the estimation methodology. (Joint work with Martin Bladt from the University of Copenhagen.)