Robustness analysis of Bitcoin confirmation times

Abstract

Bitcoin payments require a random amount of time to get confirmed (i.e. to be grouped by the miners into a block and to be added to the Bitcoin blockchain). In [8, 11], the authors propose the modelling of the Bitcoin confirmation time by the so-called time to ruin of the Cramer-Lundberg (CL) model. This provides off-the-shelf results directly aimed at predicting the confirmation time. However, analyses suggest that the data may not fully conform with the CL model assumptions. In this manuscript, we show by means of a robustness analysis that the time to ruin of a CL model is near insensitive to small changes in the model assumptions and illustrate that the proposed heuristic model can be used to accurately predict the confirmation times even when the data deviate (to a small degree) from the model assumptions.