Methods for generating coherent distortion risk measures

2018 ◽  
Vol 13 (2) ◽  
pp. 400-416
Author(s):  
Ranadeera G.M. Samanthi ◽  
Jungsywan Sepanski
Keyword(s):  
Closed Form ◽  
Parameter Space ◽  
Risk Measures ◽  
Distribution Functions ◽  
Distortion Functions ◽  
Log Normal ◽  
Parameter Values ◽  
Composite Distribution ◽  
Distortion Risk Measures

AbstractThis 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.

scholarly journals Distortion risk measures, ROC curves, and distortion divergence

2018 ◽  
Vol 35 (1-2) ◽  
pp. 35-50
Author(s):  
Johannes M. Schumacher
Keyword(s):  
Operating Characteristic ◽  
Risk Measures ◽  
Roc Curves ◽  
Probability Measures ◽  
Distortion Functions ◽  
Simple Alternative ◽  
Measures Of Risk ◽  
New Interpretation ◽  
The One ◽  
Distortion Risk Measures

AbstractDistortion functions are employed to define measures of risk. Receiver operating characteristic (ROC) curves are used to describe the performance of parametrized test families in testing a simple null hypothesis against a simple alternative. This paper provides a connection between distortion functions on the one hand, and ROC curves on the other. This leads to a new interpretation of some well-known classes of distortion risk measures, and to a new notion of divergence between probability measures.

scholarly journals New risk measures for variance distortion and catastrophic financial risk measures

2021 ◽  
Vol 25 (6) ◽  
pp. 165-184
Author(s):  
V. B. Minasyan
Keyword(s):  
Risk Management ◽  
Financial Risk ◽  
Risk Measures ◽  
Financial Risks ◽  
Large Set ◽  
Business Risk ◽  
Distortion Functions ◽  
Significant Area ◽  
Theoretical Risk ◽  
Distortion Risk Measures

In recent years, expectation distortion risk measures have been widely used in financial and insurance applications due to their attractive properties. The author introduced two new classes of financial risk measures “VaR raised to the power of t” and “ES raised to the power of t” in his works and also investigated the issue of the belonging of these risk measures to the class of risk measures of expectation distortion, and described the corresponding distortion functions. The aim of this study is to introduce a new concept of variance distortion risk measures, which opens up a significant area for investigating the properties of these risk measures that may be useful in applications. The paper proposes a method of finding new variance distortion risk measures that can be used to acquire risk measures with special properties. As a result of the study, it was found that the class of risk measures of variance distortion includes risk measures that are in a certain way related to “VaR raised to the power of t” and “ES raised to the power of t” measures. The article describes the composite method for constructing new variance distortion functions and corresponding distortion risk measures. This method is used to build a large set of examples of variance distortion risk measures that can be used in assessing certain financial risks of a catastrophic nature. The author concludes that the study of the variance distortion risk measures introduced in this paper can be used both for the development of theoretical risk management methods and in the practice of business risk management in assessing unlikely risks of high catastrophe.

scholarly journals First Light And Reionization Epoch Simulations (FLARES) – I. Environmental dependence of high-redshift galaxy evolution

2020 ◽  
Vol 500 (2) ◽  
pp. 2127-2145
Author(s):  
Christopher C Lovell ◽  
Aswin P Vijayan ◽  
Peter A Thomas ◽  
Stephen M Wilkins ◽  
David J Barnes ◽  
...  
Keyword(s):  
Galaxy Evolution ◽  
Galaxy Formation ◽  
Dynamic Range ◽  
High Redshift ◽  
Formation Rate ◽  
Mass Function ◽  
Distribution Functions ◽  
Large Area ◽  
Composite Distribution ◽  
Environmental Dependence

ABSTRACT We introduce the First Light And Reionisation Epoch Simulations (FLARES), a suite of zoom simulations using the EAGLE model. We resimulate a range of overdensities during the Epoch of Reionization (EoR) in order to build composite distribution functions, as well as explore the environmental dependence of galaxy formation and evolution during this critical period of galaxy assembly. The regions are selected from a large $(3.2 \, \mathrm{cGpc})^{3}$ parent volume, based on their overdensity within a sphere of radius 14 h−1 cMpc. We then resimulate with full hydrodynamics, and employ a novel weighting scheme that allows the construction of composite distribution functions that are representative of the full parent volume. This significantly extends the dynamic range compared to smaller volume periodic simulations. We present an analysis of the galaxy stellar mass function (GSMF), the star formation rate distribution function (SFRF), and the star-forming sequence (SFS) predicted by FLARES, and compare to a number of observational and model constraints. We also analyse the environmental dependence over an unprecedented range of overdensity. Both the GSMF and the SFRF exhibit a clear double-Schechter form, up to the highest redshifts (z = 10). We also find no environmental dependence of the SFS normalization. The increased dynamic range probed by FLARES will allow us to make predictions for a number of large area surveys that will probe the EoR in coming years, carried out on new observatories such as Roman and Euclid.

scholarly journals Dependence modelling in multivariate claims run-off triangles

2012 ◽  
Vol 7 (1) ◽  
pp. 3-25 ◽  
Author(s):  
Michael Merz ◽  
Mario V. Wüthrich ◽  
Enkelejd Hashorva
Keyword(s):  
Closed Form ◽  
Central Issue ◽  
Normal Model ◽  
Closed Form Solutions ◽  
Prediction Uncertainty ◽  
Run Off ◽  
Classical Models ◽  
Dependence Modelling ◽  
Log Normal ◽  
Dependence Structures

AbstractA central issue in claims reserving is the modelling of appropriate dependence structures. Most classical models cannot cope with this task. We define a multivariate log-normal model that allows to model both, dependence between different sub-portfolios and dependence within sub-portfolios such as claims inflation. In this model we derive closed form solutions for claims reserves and the corresponding prediction uncertainty.

Discrete Distribution Functions for Log-Normal Moments

2020 ◽  
pp. 1-21
Author(s):  
Catherine M. Bonan-Hamada ◽  
William B. Jones ◽  
W. J. Thron ◽  
Arne Magnus
Keyword(s):  
Discrete Distribution ◽  
Distribution Functions ◽  
Log Normal
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