Department of Mathematics
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 T-a,T-b(t), which is the total length of the 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 T-a,T-b(t). Explicit results are then given for the special case that claim sizes are exponentially distributed. The classical model is discussed in detail.
Occupation time, Piecewise deterministic Markov process, Risk theory, Duration of negative surplus, Ruin
Source Publication Title
Copyright © 2002 by Marcel Dekker, Inc.
Link to Publisher's Edition
Chiu, S., & Yin, C. (2002). On occupation times for a risk process with reserve-dependent premium. Stochastic Models, 18 (2), 245-255. https://doi.org/10.1081/STM-120004466