The distortion principle for insurance pricing: properties, identification and robustness

Debora Daniela Escobar; Georg Ch. Pflug

doi:10.1007/s10479-018-3119-1

The distortion principle for insurance pricing: properties, identification and robustness

Debora Daniela Escobar^*, Georg Ch. Pflug

^*Corresponding author for this work

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

8 Citations (Scopus)

13 Downloads (Pure)

Abstract

Distortion (Denneberg in ASTIN Bull 20(2):181–190, 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness w.r.t. ambiguity of the loss distribution. Ambiguity is measured by the Wasserstein distance. We study variances of distances for probability models and identify some worst case distributions. In addition to the direct problem we also investigate the inverse problem, that is how to identify the distortion density on the basis of observations of insurance premia.

Original language	English
Pages (from-to)	771-794
Number of pages	24
Journal	Annals of Operations Research
Volume	292
DOIs	https://doi.org/10.1007/s10479-018-3119-1
Publication status	Published - Sept 2020

Keywords

Ambiguity
Distortion premium
Dual representation
Premium prices
Risk measures
Wasserstein distance

Access to Document

10.1007/s10479-018-3119-1Licence: CC BY

Download pdf
© The Author(s) 2018
Final published version, 944 KBLicence: CC BY

Cite this

@article{d04151608bee4f2d96428a9b0089552d,

title = "The distortion principle for insurance pricing: properties, identification and robustness",

abstract = "Distortion (Denneberg in ASTIN Bull 20(2):181–190, 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness w.r.t. ambiguity of the loss distribution. Ambiguity is measured by the Wasserstein distance. We study variances of distances for probability models and identify some worst case distributions. In addition to the direct problem we also investigate the inverse problem, that is how to identify the distortion density on the basis of observations of insurance premia.",

keywords = "Ambiguity, Distortion premium, Dual representation, Premium prices, Risk measures, Wasserstein distance",

author = "Escobar, {Debora Daniela} and Pflug, {Georg Ch.}",

year = "2020",

month = sep,

doi = "10.1007/s10479-018-3119-1",

language = "English",

volume = "292",

pages = "771--794",

journal = "Annals of Operations Research",

issn = "0254-5330",

publisher = "Springer",

}

TY - JOUR

T1 - The distortion principle for insurance pricing: properties, identification and robustness

AU - Escobar, Debora Daniela

AU - Pflug, Georg Ch.

PY - 2020/9

Y1 - 2020/9

N2 - Distortion (Denneberg in ASTIN Bull 20(2):181–190, 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness w.r.t. ambiguity of the loss distribution. Ambiguity is measured by the Wasserstein distance. We study variances of distances for probability models and identify some worst case distributions. In addition to the direct problem we also investigate the inverse problem, that is how to identify the distortion density on the basis of observations of insurance premia.

AB - Distortion (Denneberg in ASTIN Bull 20(2):181–190, 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness w.r.t. ambiguity of the loss distribution. Ambiguity is measured by the Wasserstein distance. We study variances of distances for probability models and identify some worst case distributions. In addition to the direct problem we also investigate the inverse problem, that is how to identify the distortion density on the basis of observations of insurance premia.

KW - Ambiguity

KW - Distortion premium

KW - Dual representation

KW - Premium prices

KW - Risk measures

KW - Wasserstein distance

U2 - 10.1007/s10479-018-3119-1

DO - 10.1007/s10479-018-3119-1

M3 - Article

SN - 0254-5330

VL - 292

SP - 771

EP - 794

JO - Annals of Operations Research

JF - Annals of Operations Research

ER -

The distortion principle for insurance pricing: properties, identification and robustness

Abstract

Keywords

Access to Document

Fingerprint

Cite this