By embedding a Markov-modulated random recurrence equation in continuous time, in this talk I will derive the Markov-modulated generalized Ornstein-Uhlenbeck process. This process turns out to be the unique solution of a stochastic differential equation driven by a bivariate Markov-additive process that will be presented and solved explicitely. Afterwards we discuss basic properties of the obtained processes such as stationarity conditions and some moments. If time permits, we may also discuss a possible application and introduce a Markov-modulated risk model with investment that generalizes Paulsen?s risk process to a Markov-switching environment.