When estimating risk from a window of historical observations, the confidence interval is inverse to the number of scenarios used, which is the length of the window. When estimating risk with exponential decay, where the relative weight of each scenario decreases with time, the confidence...

We show how to mix machine learning signals such as kernel smoothing and fuzzy memberships via the Entropy Pooling approach by Meucci (2008). We illustrate a case study, where we overlay an exponentially time-decayed prior to a pseudo-Gaussian kernel that emphasizes market scenarios where...

In the Flexible Probabilities approach, given the historical distribution (histogram) of the returns of a portfolio, we can stress-test the portfolio under different time periods and market environments, by adjusting the relative weights (Flexible Probabilities) of the historical returns in the...