On occupation times for a risk process with reserve-dependent premium

Consider a risk reserve process under which the reserve can generate interest. For constants a and b such that a<b, we study the occupation time Ta,b(t), which is the total length of time intervals up to time t during which the reserve is between a and b. We first present a general formula for piecewise deterministic Markov processes, which will be used for the computation of the Laplace transform of Ta,b(t). Explicit results are then given for the special case that claim sizes are exponentially distributed. The classical model is discussed in detail.