The influence of perceived stock value price histories in the mean–variance-instability model

The model introduced by H. Talpaz, A. Harpaz and J.B. Penson extends the mean–variance model introducing the concept of instability. In this way it is possible to see an investor's attitude towards predicted instability. In this paper we show how optimisation procedures based on penalty (or preferred) weighted instability matrices can be interpreted in terms of real time utility functions which depend on an ‘actual’ and a ‘remembered’ time series due to fading memory. This approach justifies some bounded normalised functions used to represent the investor's preference between the irregular frequency fluctuations.