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

Escobar, Debora Daniela; Pflug, Georg Ch.

doi:10.1007/s10479-018-3119-1

Cited by 18 publications

(4 citation statements)

References 33 publications

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“…In this section, we assume that the true weighting function of a decision maker is roughly known either based on empirical data or based on a subjective judgement. For example, Escobar and Pflug [14] propose an effective approach to construct a step-like distortion function with empirical data and use it to approximate the true unknown distortion/weighting function in an insurance premium calculation model. We call such an estimated weighting function as nominal weighting function.…”

Section: Construction Of Ambiguity Set W Of Weighting Functionsmentioning

confidence: 99%

Preference Robust Generalized Shortfall Risk Measure Based on the Cumulative Prospect Theory When the Value Function and Weighting Functions Are Ambiguous

Zhang¹,

Xu²

2021

Preprint

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The utility-based shortfall risk (SR) measure introduced by Fölmer and Schied [15] has been recently extended by Mao and Cai [29] to cumulative prospect theory (CPT) based SR in order to better capture a decision maker's utility/risk preference. In this paper, we consider a situation where information on the value function and/or the weighting functions in the CPT based SR is incomplete. Instead of using partially available information to construct an approximate value function and weighting functions, we propose a robust approach to define a generalized shortfall risk which is based on a tuple of the worst case value/weighting functions from ambiguity sets of plausible value/weighting functions identified via available information. The ambiguity set may be constructed with elicited preference information (e.g. pairwise comparison questionnaires) and subjective judgement, and the ambiguity reduces as more and more preference information is obtained. Under some moderate conditions, we demonstrate how the subproblem of the robust shortfall risk measure can be calculated by solving a linear programming problem. To examine the performance of the proposed robust model and computational scheme, we carry out some numerical experiments and report preliminary test results. This work may be viewed as an extension of recent research of preference robust optimization models to the CPT based SR.

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Section: Construction Of Ambiguity Set W Of Weighting Functionsmentioning

confidence: 99%

Preference Robust Generalized Shortfall Risk Measure Based on the Cumulative Prospect Theory When the Value Function and Weighting Functions Are Ambiguous

Zhang¹,

Xu²

2021

Preprint

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“…Huang and Meng [ 5 ] corrected the skewness and heavy tail problem of insurance loss using a Bayesian nonparametric regression model based on Gaussian distribution. Escobar and Pflug [ 6 ] determined the worst case of insurance distribution with the distance variance of the probability model. These methods can produce more appropriate empirical results.…”

Section: Introductionmentioning

confidence: 99%

Study on Bayesian Skew-Normal Linear Mixed Model and Its Application in Fire Insurance

et al. 2023

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Fire insurance is a crucial component of property insurance, and its rating depends on the forecast of insurance loss claim data. Fire insurance loss claim data have complicated characteristics such as skewness and heavy tail. The traditional linear mixed model is commonly difficult to accurately describe the distribution of loss. Therefore, it is crucial to establish a scientific and reasonable distribution model of fire insurance loss claim data. In this study, the random effects and random errors in the linear mixed model are firstly assumed to obey the skew-normal distribution. Then, a skew-normal linear mixed model is established using the Bayesian MCMC method based on a set of U.S. property insurance loss claims data. Comparative analysis is conducted with the linear mixed model of logarithmic transformation. Afterward, a Bayesian skew-normal linear mixed model for Chinese fire insurance loss claims data is designed. The posterior distribution of claim data parameters and related parameter estimation are employed with the R language JAGS package to obtain the predicted and simulated loss claim values. Finally, the optimization model in this study is used to determine the insurance rate. The results demonstrate that the model established by the Bayesian MCMC method can overcome data skewness, and the fitting and correlation with the sample data are better than the log-normal linear mixed model. Hence, it can be concluded that the distribution model proposed in this paper is reasonable for describing insurance claims. This study innovates a new approach for calculating the insurance premium rate and expands the application of the Bayesian method in the fire insurance field.

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“…This approach has been pursued e.g., for distributionally robust portfolio optimisation over neighborhoods of a reference probability measure by [31,40,28,16] or more generally for stochastic programming problems as in [29,5,3,35,32]. For the special case of distributional robust versions of Value at Risk (VaR) we refer to [27] and [26], where the risk measure is robustified via the concept of sublinear expectations, and also by [10], where the supremum of VaR over a set of possible joint distributions with prespecified marginals is computed.…”

mentioning

confidence: 99%

Risk measures under model uncertainty: A Bayesian viewpoint

Cuchiero,

Gazzani,

Klein

2023

FMF

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We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain minimax inequality is actually an equality. We then provide conditions under which the corresponding robust risk measures, being defined as the supremum over all risk measures induced by a set of probability measures, can be represented classically in terms of one single probability measure. We focus in particular on the mixture probability measure obtained via mixing over a set of probability measures using some prior, which represents for instance the regulator's beliefs. The classical representation in terms of the mixture probability measure can then be interpreted as a Bayesian approach to robust risk measures.

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

Cited by 18 publications

References 33 publications

Preference Robust Generalized Shortfall Risk Measure Based on the Cumulative Prospect Theory When the Value Function and Weighting Functions Are Ambiguous

Preference Robust Generalized Shortfall Risk Measure Based on the Cumulative Prospect Theory When the Value Function and Weighting Functions Are Ambiguous

Study on Bayesian Skew-Normal Linear Mixed Model and Its Application in Fire Insurance

Risk measures under model uncertainty: A Bayesian viewpoint

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