scholarly journals Distortion risk measures for sums of random variables

2004 ◽  
Vol 26 (4) ◽  
pp. 631-641
Author(s):  
Grzegorz Darkiewicz ◽  
Jan Dhaene ◽  
Marc Goovaerts
Keyword(s):  
Risk Measures ◽  
Random Variables ◽  
Sums Of Random Variables ◽  
Distortion Risk Measures

Series expansions for convolutions of Pareto distributions

2015 ◽  
Vol 32 (1) ◽  
Author(s):  
Quang Huy Nguyen ◽  
Christian Y. Robert
Keyword(s):  
Infinite Series ◽  
Asymptotic Expansions ◽  
Value At Risk ◽  
Risk Measures ◽  
Random Variables ◽  
Series Expansions ◽  
Sums Of Random Variables ◽  
Scale Parameters ◽  
Pareto Distributions ◽  
Higher Order Terms

AbstractAsymptotic expansions for the tails of sums of random variables with regularly varying tails are mainly derived in the case of identically distributed random variables or in the case of random variables with the same tail index. Moreover, the higher-order terms are often given under the condition of existence of a moment of the distribution. In this paper, we obtain infinite series expansions for convolutions of Pareto distributions with non-integer tail indices. The Pareto random variables may have different tail indices and different scale parameters. We naturally find the same constants for the first terms as given in the previous asymptotic expansions in the case of identically distributed random variables, but we are now able to give the next additional terms. Since our series expansion is not asymptotic, it may be also used to compute the values of quantiles of the distribution of the sum as well as other risk measures such as the Tail Value at Risk. Examples of values are provided for the sum of at least five Pareto random variables and are compared to those determined via previous asymptotic expansions or via simulations.

Equivalent Distortion Risk Measures on Moment Spaces

2018 ◽  
Author(s):  
Dries Cornilly ◽  
Steven Vanduffel
Keyword(s):  
Risk Measures ◽  
Moment Spaces ◽  
Distortion Risk Measures

Estimation of Distortion Risk Measures

2013 ◽  
Vol 12 (1) ◽  
pp. 213-235 ◽  
Author(s):  
H. Tsukahara
Keyword(s):  
Risk Measures ◽  
Distortion Risk Measures

First-order autoregressive gamma sequences and point processes

1980 ◽  
Vol 12 (3) ◽  
pp. 727-745 ◽  
Author(s):  
D. P. Gaver ◽  
P. A. W. Lewis
Keyword(s):  
Parameter Estimation ◽  
Point Processes ◽  
Random Variables ◽  
Innovation Process ◽  
Sums Of Random Variables ◽  
First Order ◽  
Wide Range ◽  
Serial Correlations ◽  
Generating Sequences ◽  
Stieltjes Transforms

It is shown that there is an innovation process {∊n} such that the sequence of random variables {Xn} generated by the linear, additive first-order autoregressive scheme Xn = pXn-1 + ∊n are marginally distributed as gamma (λ, k) variables if 0 ≦p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.

Sign in / Sign up

Export Citation Format

Share Document