Methods for generating coherent distortion risk measures

Ranadeera G.M. Samanthi; Jungsywan Sepanski

doi:10.1017/S1748499518000258

Methods for generating coherent distortion risk measures

Ranadeera G.M. Samanthi, Jungsywan Sepanski

Statistics, Actuarial & Data Sciences

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

This paper presents methods for generating new distortion functions utilising distribution functions and composite distribution functions. To ensure the coherency of the corresponding distortion risk measures, the concavity of the proposed distortion functions is established by restricting the parameter space of the generating distribution. Closed-form expressions for risk measures are derived for some cases. Numerical and graphical results are presented to demonstrate the effects of parameter values on the risk measures for exponential, Pareto and log-normal losses. In addition, we apply the proposed distortion functions to derive risk measures for a segregated fund guarantee.

Original language	English
Pages (from-to)	400-416
Number of pages	17
Journal	Annals of Actuarial Science
Volume	13
Issue number	2
DOIs	https://doi.org/10.1017/S1748499518000258
State	Published - Sep 1 2019

Keywords

Distortion function
Exponential-exponential distortion
Kumaraswamy distortion
Risk measure
Truncated normal distortion

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abstract = "This paper presents methods for generating new distortion functions utilising distribution functions and composite distribution functions. To ensure the coherency of the corresponding distortion risk measures, the concavity of the proposed distortion functions is established by restricting the parameter space of the generating distribution. Closed-form expressions for risk measures are derived for some cases. Numerical and graphical results are presented to demonstrate the effects of parameter values on the risk measures for exponential, Pareto and log-normal losses. In addition, we apply the proposed distortion functions to derive risk measures for a segregated fund guarantee.",

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AB - This paper presents methods for generating new distortion functions utilising distribution functions and composite distribution functions. To ensure the coherency of the corresponding distortion risk measures, the concavity of the proposed distortion functions is established by restricting the parameter space of the generating distribution. Closed-form expressions for risk measures are derived for some cases. Numerical and graphical results are presented to demonstrate the effects of parameter values on the risk measures for exponential, Pareto and log-normal losses. In addition, we apply the proposed distortion functions to derive risk measures for a segregated fund guarantee.

KW - Distortion function

KW - Exponential-exponential distortion

KW - Kumaraswamy distortion

KW - Risk measure

KW - Truncated normal distortion

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JF - Annals of Actuarial Science

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Methods for generating coherent distortion risk measures

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Keywords

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