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Methods for generating coherent distortion risk measures

Published online by Cambridge University Press:  29 August 2018

Ranadeera G.M. Samanthi  and
Jungsywan Sepanski
Ranadeera G.M. Samanthi*
Affiliation:
Department of Mathematics, Central Michigan University, Mt. Pleasant, MI 48859, USA
Jungsywan Sepanski
Affiliation:
Department of Mathematics, Central Michigan University, Mt. Pleasant, MI 48859, USA
*
*Correspondence to: Ranadeera G.M. Samanthi, Department of Mathematics, Central Michigan University, Mt. Pleasant, MI 48859, USA. E-mail: saman1rg@cmich.edu
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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.

Keywords

Risk measureDistortion functionKumaraswamy distortionTruncated normal distortionExponential-exponential distortion
Type
Review
Information
Annals of Actuarial Science , Volume 13 , Issue 2 , September 2019 , pp. 400 - 416
Copyright
© Institute and Faculty of Actuaries 2018 

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