Abstract:Understanding the attitude to risk implicit within a risk measure sheds some light on the way in which decision makers perceive losses. In this paper, a two-stage strategy is developed to characterize the underlying risk attitude involved in a risk evaluation, when executed by the family of distortion risk measures. First, we show that aggregation indicators defined for discrete Choquet integrals provide information about the implicit global risk attitude of the agent. Second, an analysis of the distortion fun… Show more
“…Goovaerts et al (2004) suggest that insurance premium principles or risk measures should be selected so that they satisfy certain properties or axioms such as monotonicity, subadditivity, positive homogeneity and translation invariance to reflect the realities of practices. Belles-Sampera et al (2016) use the area under the distortion function to quantify the global risk attitude, with decision-makers classifies as risk tolerant, risk neutral or risk intolerant if the corresponding areas are more than half, half and less than half, respectively. The proposed coherent distortions lead to risk measures satisfying the four coherency axioms.…”
Section: Discussionmentioning
confidence: 99%
“…Belles-Sampera et al (2016) also suggest graphing the quotient between the distortion function ψ ( u ) and the identity function u for analysis of the risk attitude locally at each u value, with quotients greater than 1, equal to 1 and less than 1 representing risk tolerant, neutral and intolerant, respectively. Figure 6 exhibits the distortion curves and the corresponding quotient curves with parameter values ( a , b )=(0.35, 5) and ( μ , σ )=(−0.5, 0.5) for the truncated normal distortion.Figure 6The distortion and quotient functions of truncated normal transform with μ =−0.5 and σ =0.5 and other transforms with parameters a =0.35 and b =5.…”
Section: Examplesmentioning
confidence: 99%
“…Figure 1 displays the concave curves of the Kumaraswamy distortion for various parameter values. Belles-Sampera et al (2016) use the area under the distortion function as a measure of global risk attitude. Note that the area under a concave curve on [0, 1] is always greater than half, and a larger area indicates a higher level of global risk tolerant attitude.…”
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.
“…Goovaerts et al (2004) suggest that insurance premium principles or risk measures should be selected so that they satisfy certain properties or axioms such as monotonicity, subadditivity, positive homogeneity and translation invariance to reflect the realities of practices. Belles-Sampera et al (2016) use the area under the distortion function to quantify the global risk attitude, with decision-makers classifies as risk tolerant, risk neutral or risk intolerant if the corresponding areas are more than half, half and less than half, respectively. The proposed coherent distortions lead to risk measures satisfying the four coherency axioms.…”
Section: Discussionmentioning
confidence: 99%
“…Belles-Sampera et al (2016) also suggest graphing the quotient between the distortion function ψ ( u ) and the identity function u for analysis of the risk attitude locally at each u value, with quotients greater than 1, equal to 1 and less than 1 representing risk tolerant, neutral and intolerant, respectively. Figure 6 exhibits the distortion curves and the corresponding quotient curves with parameter values ( a , b )=(0.35, 5) and ( μ , σ )=(−0.5, 0.5) for the truncated normal distortion.Figure 6The distortion and quotient functions of truncated normal transform with μ =−0.5 and σ =0.5 and other transforms with parameters a =0.35 and b =5.…”
Section: Examplesmentioning
confidence: 99%
“…Figure 1 displays the concave curves of the Kumaraswamy distortion for various parameter values. Belles-Sampera et al (2016) use the area under the distortion function as a measure of global risk attitude. Note that the area under a concave curve on [0, 1] is always greater than half, and a larger area indicates a higher level of global risk tolerant attitude.…”
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.
“…The linear combination of the GlueVaR risk measure allows for defining a particular investor in terms on his attitude towards risk (Belles-Sampera et al 2015). If an investor selects weights ( 1 , 2 ) = (1,0) then he represents highly conservative attitude towards risk.…”
Investing in the economic world, characterized by a high level of uncertainty and volatility, entails a higher level of risk related to investment. One of the most commonly used risk measure is Value-at-Risk. However, despite the ease of calculation and interpretation, this measure suffers from a significant drawbackit is not subadditive. This property is the key issue in terms of portfolio diversification. Another risk measure, which meets this assumption, has been proposed -Conditional Value-at-Risk, defined as a conditional loss beyond Value-at-Risk. However, the choice of a risk measure is an individual decision of an investor and it is directly related to his attitudes to risk. In this paper the new risk measure is proposed -the GlueVaR risk measure, which can be defined as a linear combination of VaR and GlueVaR. It allows for calculating the level of investment loss depending on investment's attitudes to risk. Moreover, GlueVaR meets the subadditivity property, therefore it may be used in portfolio risk assessment. The application of the GlueVaR risk measure is presented for the non-ferrous metals market.
“…The merits of the DRM-based model are multi-fold. First, it is known that the perception of risk DRM reflects is more consistent with human behavior than what the traditional expected utility paradigm offers (see Belles-Sampera et al, 2016 for more information). Second, due to the translation invariance of DRM, risk minimization is synonymous with profit maximization.…”
The formulation of optimal reinsurance policies that take various practical constraints into account is a problem commonly encountered by practitioners. In the context of a distortion-risk-measure-based optimal reinsurance model without moral hazard, this article introduces and employs a variation of the Neyman–Pearson Lemma in statistical hypothesis testing theory to solve a wide class of constrained optimal reinsurance problems analytically and expeditiously. Such a Neyman–Pearson approach identifies the unit-valued derivative of each ceded loss function as the test function of an appropriate hypothesis test and transforms the problem of designing optimal reinsurance contracts to one that resembles the search of optimal test functions achieved by the classical Neyman–Pearson Lemma. As an illustration of the versatility and superiority of the proposed Neyman–Pearson formulation, we provide complete and transparent solutions of several specific constrained optimal reinsurance problems, many of which were only partially solved in the literature by substantially more difficult means and under extraneous technical assumptions. Examples of such problems include the construction of the optimal reinsurance treaties in the presence of premium budget constraints, counterparty risk constraints and the optimal insurer–reinsurer symbiotic reinsurance treaty considered recently in Cai et al. (2016).
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