In this paper, we study bonus systems in an open portfolio, i.e. we conside
r that a policyholder can transfer his policy to a different insurance comp
any at any time. We make use of inhomogeneous Markov chains to model the sy
stem and show, under reasonable assumptions, that the stationary distributi
on is independent of the market shares, and is easily calculated. (C) 2001
Elsevier Science B.V. All rights reserved.