Yet another breakdown point notion: EFSBP - illustrated at scale-shape models

The breakdown point in its different variants is one of the central notions to quantify the global robustness of a procedure. We propose a simple supplementary variant which is useful in situations where we have no obvious or only partial equivariance: Extending the Donoho and Huber(1983) Finite Sample Breakdown Point, we propose the Expected Finite Sample Breakdown Point to produce less configuration-dependent values while still preserving the finite sample aspect of the former definition. We apply this notion for joint estimation of scale and shape (with only scale-equivariance available), exemplified for generalized Pareto, generalized extreme value, Weibull, and Gamma distributions. In these settings, we are interested in highly-robust, easy-to-compute initial estimators; to this end we study Pickands-type and Location-Dispersion-type estimators and compute their respective breakdown points.Comment: 21 pages, 4 figure

Robust high-dimensional precision matrix estimation

The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in high-dimensions, it cannot be used to obtain a precision matrix estimator. A popular high-dimensional estimator is the graphical lasso, but it lacks robustness. We consider the high-dimensional independent contamination model. Here, even a small percentage of contaminated cells in the data matrix may lead to a high percentage of contaminated rows. Downweighting entire observations, which is done by traditional robust procedures, would then results in a loss of information. In this paper, we formally prove that replacing the sample covariance matrix in the graphical lasso with an elementwise robust covariance matrix leads to an elementwise robust, sparse precision matrix estimator computable in high-dimensions. Examples of such elementwise robust covariance estimators are given. The final precision matrix estimator is positive definite, has a high breakdown point under elementwise contamination and can be computed fast

The optimal payoff for a Yaari investor

Yaari's dual theory of choice under risk is the natural counterpart of expected utility theory. While optimal payoff choice for an expected utility maximizer is well studied in the literature, less is known about the optimal payoff for a Yaari investor. We perform a fairly general analysis and derive optimal payoffs in a variety of relevant cases. As a main contribution, we provide the optimal payoff for a Yaari investor under a variance constraint; thus, extending mean–variance optimization to distorted expectation–variance optimization. We also derive the optimal payoff for an investor who aims to outperform an external benchmark under the requirement that the payoff stays in the neighbourhood of this benchmark

Properties of the Margrabe Best-of-two strategy to tactical asset allocation

© 2019 Elsevier Inc. The Margrabe Best-of-two (MBo2) strategy is a rule-based dynamic investment solution for the two-asset allocation problem. Its typical implementation involves yearly rebalancing the portfolio weights to 50–50 between a low-risk and high-risk asset. It uses intra-year weight adjustments to chase the momentum of the best performing asset by replicating the Margrabe formula for the value of a European option to exchange an asset for another asset at year-end. In practice, this means that the Margrabe portfolio allocation benefits from the upside potential of the high-risk asset and the downside protection from the low-risk asset. The MBo2 allocation depends on the assets’ prices, their return volatilities, and correlation, as well as the remaining time until year-end. In this paper, we derive analytical formulae and use simulations to provide insights into the sensitivity of the strategy's weights and performance to these input parameters. We also report the results of an extensive out-of-sample evaluation for the MBo2 strategy applied to the bond–equity, real estate–equity, and world equity–emerging market equity portfolio allocation problems.status: Published onlin