Distortion Risk Research Articles

On tail-risk measures for non-integrable heavy-tailed random variables

The assessment of risk for heavy-tailed distributions is a crucial question in various fields of application. An important family of risk measures is provided by the class of distortion risk (DR) measures which encompasses the Value-at-Risk and the Tail-Value-at-Risk measures. The Tail-Value-at-Risk is a coherent risk measure (which is not the case for the Value-at-Risk) but it is defined only for integrable quantile functions that is to say for heavy-tailed distributions with a tail index smaller than 1. Moreover, it is a matter of fact that the performance of the empirical estimator is strongly deteriorated when the tail index becomes close to 1. The main contribution is the introduction and the estimation of a new risk measure which is defined for all heavy-tailed distributions and which is tail-equivalent to a coherent DR measure when the tail of the underlying distribution is not too heavy. Its finite sample performance is discussed on a fire claims dataset.

Risk Constraints in the Context of Big Data and Optimization of a Virtuous Interaction Mechanism for Insurance Management Based on Distorted Risk Metrics.

A relevant definition of big data technology has been released by relevant research institutes in China. Big data technology is defined as follows: big data technology is a digitally important productivity factor in the network era; big data technology is based on network technology, statistical technology, and mathematical technology; big data technology, as a carrier of network technology, should be integrated with various industries and technologies other than contemporary ones in order to achieve better informatization and industrialization. In the context of the new crown epidemic in 2020, China's big data technology continues to grow steadily, with a total value of 39.2 trillion yuan, accounting for 38.6% of GDP. This paper investigates the risk constraint in the context of big data and optimizes the benign interaction mechanism of insurance management based on distorted risk metrics in this context. The current situation of insurance risk is investigated through a profound discussion of theories in this paper and through research methods such as distortion risk metrics and SQL Server database management. It is found that the overall situation of insurance industry development in the era of digital economy is not optimistic and so on. And relevant suggestions are made in the conclusion.

E-DMDAV: A new privacy preserving algorithm for wearable enterprise information systems

ABSTRACTWearable devices have been widely used in many fields to improve the quality of people’s lives. More and more data on individuals and businesses are collected by statistical organizations though those devices. Almost all of this data holds confidential information. Statistical Disclosure Control (SDC) seeks to protect statistical data in such a way that it can be released without giving away confidential information that can be linked to specific individuals or entities. The MDAV (Maximum Distance to Average Vector) algorithm is an efficient micro-aggregation algorithm belonging to SDC. However, the MDAV algorithm cannot survive homogeneity and background knowledge attacks because it was designed for static numerical data. This paper proposes a systematic dynamic-updating anonymity algorithm based on MDAV called the e-DMDAV algorithm. This algorithm introduces a new parameter and a table to ensure that the k records in one cluster with the range of the distinct values in each cluster is no less than e for numerical and non-numerical datasets. This new algorithm has been evaluated and compared with the MDAV algorithm. The simulation results show that the new algorithm outperforms MDAV in terms of minimizing distortion and disclosure risk with a similar computational cost.

Mean and Risk Densities and Their Application to Risk Management

This paper proposes a framework to analyze mean and distortion risk across layers forming a random loss. Layers are standard insurance and financial constructs representing insurance coverage, capital shortfall, derivative payouts and debt tranches. Layers are expressed using percentiles or Value-at-Risk which adjust to the shape and scale of the probability distribution. The framework yields insights and solutions to common risk management problems which are difficult or awkward to solve using standard statistical methods.