Modeling volatility, or predictable changes over time and space in a variable, is crucial in the natural and social sciences. Life can be volatile, and anything that matters, and which changes over time and space, involves volatility. Without volatility, many temporal and spatial variables would...

We compare Value at Risk (VaR) and Expected Shortfall (ES) following a Stochastic Dominance (SD) approach frequently used to order distributions in terms of welfare and in portfolio selection. Basel Committee on Banking Supervision (BCBS) recommends bank risk managers to shift the current...

In the physical sciences, order and disorder refer to the presence or absence of some symmetry or correlation in a many-particle system. It follows that it is important to examine whether there is any regularity hidden in the phase transition of the disorder-order relationship. In this paper a...