A discussion on Buhlmann’s criterion for asset valuation

In this paper, we consider the criterion of Buhlmann [N. Am. Actuarial J. 1 (1997) 100] for asset valuation. The limiting behavior of the trend of the valuation compared with the real development is studied for both i.i.d. growth rates and Markov dependent growth rates. The average sojourn time within Buhlmann’s band is assessed for independent growth rates by the technique of Wald’s sequential analysis. A continuous asset model discussed in [Insur. Math. Econ. 24 (1999) 3] is also studied with this criterion. From this continuous model, we will see some interesting links of this topic with ruin theory.