This paper studies the behavior of the conventional measures of skewness and kurtosis when the data generator process is a distribution which does not possess variance or third or fourth moment and assesses the robustness of the alternative measures for these particular cases. I first show that...

The information contained in PP-plots is transformed into a single number. The resulting Harmonic Mass (HM) index is distribution free and its sample counterpart is shown to be consistent. For a wide class of CDFs the exact analytical expression of the distribution of the sample HM index is...

We describe characteristics of various risk measures (Value-at-Risk, Expected Shortfall, etc.) that are used to analyze and quantify the tail risk exposure, and discuss their relative strengths and weaknesses. Emphasis is placed on presenting and comparing methodologies to compute and backtest...

We develop the idea of using Monte Carlo sampling of random portfolios to solve portfolio investment problems. We explore the need for more general optimization tools, and consider the means by which constrained random portfolios may be generated. DeVroye's approach to sampling the interior of a...

This note discusses some problems possibly arising when approximating via MonteCarlo simulations the distributions of goodness-of-fit test statistics based on the empirical distribution function. We argue that failing to reestimate unknown parameters on each simulated Monte-Carlo sample - and...

In order to better capture empirical phenomena, research on option price and implied volatility modeling increasingly advocates the use of nonparametric methods over simple functional forms. This, however, comes at a price, since these methods require dense observations to yield sensible...

We study the out-of-sample properties of robust empirical optimization problems with smooth φ-divergence penalties and smooth concave objective functions, and develop a theory for data-driven calibration of the non-negative “robustness parameter” δ that controls the size of the deviations...