The estimation of the holding periods of financial products has to be done in a dynamic process in which the size of the observation time interval influences the result. Small intervals will produce smaller average holding periods than bigger ones. The approach developed in this paper offers the possibility of estimating this average independently of the size of this time interval. This method is demonstrated on the example of two distributions, based on the exponential and the geometric probability functions. The estimation will be found by maximizing the likelihood function.
The effect on the mean-variance space of restrictions on a variable is investigated in this
paper. A restriction may be the placing of upper and lower bounds on a variable.
Another limitation is the loss of the continuity of a variable.
Average marks for Examinations are considered in an application of this limited meanvariance
space. In this case, the bounds are given by the highest and the lowest possible mark (e.g. 1.0 and 5.0). The limitation of the mean-variance space depends on the number of students who participate in the examination. The restriction of the loss of continuity is shown by the use of discrete marks (e.g. 1.0, 1.3, 1.7, 2.0, …). Furthermore,
the Target-Shortfall-Probability lines are integrated into the mean-variance space. These
lines are used to indicate the proportion of students who have good or very good marks in the examination. In financial markets, Target-Shortfall-Probability is used as a risk criterion.