We introduce a family of Capital allocation rules (C.A.R) based on the dual representation for risk measures and inspired to the Aumann-Shapley allocation principle. These rules extend the one of Denault and Kalkbrener (for coherent risk measures) and the one of Tsanakas (convex case), to the...

The optimization of a large random portfolio under the Expected Shortfall risk measure with an ℓ₂ regularizer is carried out by analytical calculation. The regularizer reins in the large sample fluctuations and the concomitant divergent estimation error, and eliminates the phase transition...

We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value at risk (CVaR) is a special case of the spectral risk measure, our algorithm solves portfolio selection problems with...

Tail risk refers to the possibility that a rare event would adversely affect the value of a portfolio in a significant manner. It became much more relevant due to recent periods of strong market turbulence.We describe how to quantify such risk, which tail risk protection strategies were...

Using a unique data set on German banks' sector specific loan exposures to the real economy and the corresponding write-offs and write-downs, we examine the impact of loan portfolio sector concentration on credit risk. By controlling for common risk factors, we separate the bank-specific...

Banks face a tradeoff between diversifying and focusing their loan portfolio. In this paper we carry out an empirical study for the German market to shed light on the question whether or not the benefits of risk sharing outweigh those of specialization. We use data from the Bundesbank's...

The Value at Risk of a portfolio differs from the sum of the Values at Risk of the portfolio's components. In this paper, we analyze the problem of how a single economic risk figure for the Value at Risk of a hypothetical portfolio composed of different commercial banks might be obtained for a...

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management...

Uncertainty is generally avoided when investing. Volatility is a popular proxy for investment uncertainty, and indeed low volatility stocks outperform high volatility stocks. However, there are also many other possible measures of uncertainty, among which are entropy and the Hurst exponent. Here...

In aftermath of the Financial Crisis, some risk management practitioners advocate wider adoption of Bayesian inference to replace Value-at-Risk (VaR) models for minimizing risk failures (Borison & Hamm, 2010). They claim reliance of Bayesian inference on subjective judgment, the key limitation...