New Classes of Distortion Risk Measures and Their Estimation

Jungsywan H. Sepanski () and Xiwen Wang
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Jungsywan H. Sepanski: Department of Statistics, Actuarial and Data Sciences, Central Michigan University, Mount Pleasant, MI 48859, USA
Xiwen Wang: Citigroup, Tampa, FL 33610, USA

Risks, 2023, vol. 11, issue 11, 1-21

Abstract: In this paper, we present a new method to construct new classes of distortion functions. A distortion function maps the unit interval to the unit interval and has the characteristics of a cumulative distribution function. The method is based on the transformation of an existing non-negative random variable whose distribution function, named the generating distribution, may contain more than one parameter. The coherency of the resulting risk measures is ensured by restricting the parameter space on which the distortion function is concave. We studied cases when the generating distributions are exponentiated exponential and Gompertz distributions. Closed-form expressions for risk measures were derived for uniform, exponential, and Lomax losses. Numerical and graphical results are presented to examine the effects of the parameter values on the risk measures. We then propose a simple plug-in estimate of risk measures and conduct simulation studies to compare and demonstrate the performance of the proposed estimates. The plug-in estimates appear to perform slightly better than the well-known L-estimates, but also suffer from biases when applied to heavy-tailed losses.

Keywords: coherent risk measure; distortion function; exponential–exponential distortion; Kumaraswamy distortion; Gompertz distortion; L-estimator; plug-in estimator (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:11:y:2023:i:11:p:194-:d:1277752

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