We propose a new backtesting framework for Expected Shortfall that could be used by the regulator. Instead of looking at the estimated capital reserve and the realised cash-flow separately, one could bind them into the secured position, for which risk measurement is much easier. Using this...

The estimation of risk measures recently gained a lot of attention, partly because of the backtesting issues of expected shortfall related to elicitability. In this work we shed a new and fundamental light on optimal estimation procedures of risk measures in terms of bias.We show that once the...

Abstract In this paper, we develop a novel methodology for estimation of risk capital allocation. The methodology is rooted in the theory of risk measures. We work within a general, but tractable class of law-invariant coherent risk measures, with a particular focus on expected shortfall. We...

In this paper we provide a mathematical illustration to an empirical fuzzy phenomena known as 20-60-20 rule. In particular we show that if a random vector follows multivariate normal distribution and we split the whole population into three groups, then this fixed ratio leads to a global...

In this paper we provide a unified and flexible framework for study of the time consistency of risk and performance measures. The proposed framework integrates existing forms of time consistency as well as various connections between them. In our approach the time consistency is studied for a...

It is shown that the the popular least squares method of option pricing converges even if the underlying is non-Markovian, the pay-offs are path dependent and with a very flexible setup for approximation of conditional expectations. The main benefit is the increase of freedom in creating...