Bonus Systems in an Open Portfolio

In this paper we study Bonus systems in an open portfolio, i.e. we consider that a policyholder can transfer his policy from our to another insurance company and vice-versa. We make use of non-homogeneous Markov chains to model the system and show, under quite fair assumptions, that the stationary distribution is independent of the market shares, and is very easily calculated.

Keywords: Bonus systems; Markov chains; stationary distribution; open model; closed model