We develop the theory of dynamic coherent risk measures (DCRMs) generated by distortion functions in discrete time setup. We provide a representation of DCRMs in terms of distortion functions, and show that this class of DCRMs coincides with a newly defined class of the so-called dynamic value at risk (dWV@R). Consequently, we discuss various types of time consistency of dWV@Rs and the associated DCAIs. At last, we apply this theory to the analysis and estimation of dWV@R.
Math is undergoing a process resultant of the increased promotion of STEM and education reform, movements which aren’t inherently negative, but the externalities associated with them seem to be. This crisis has been discussed before, perhaps most famously with Lockhart’s lament in 2002, a 25-page essay criticizing the method of which math is taught, later being published as a longer book in 2008, and since having discussion about this subject permeate throughout the field; But it seems that is exactly all that has happened: discussion, or in other cases, system reformations made in vain. In this talk, my goal will be to recapitulate the points made by Paul Lockhart, some additional problems seen with increasing statistics, and demonstrated steps that can be taken both in the “short-term” and “long-term” to fight this issue. The work here is not novel, as this is merely a compilation of extant and past research.