Maturity Guarantees Revisited: Allowing for Extreme Stochastic Fluctuations using Stable Distributions

1997 ◽  
Vol 3 (2) ◽  
pp. 411-482 ◽  
Author(s):  
G.S. Finkelstein
Keyword(s):  
Stable Distribution ◽  
Working Party ◽  
Stable Distributions ◽  
Investment Model ◽  
Stochastic Fluctuations ◽  
Stable Family ◽  
Family Of Distributions

ABSTRACTThe paper examines the suitability of the stable family of distributions with the Maturity Guarantees Working Party's stochastic investment model (Ford et al, 1980). It then examines the effect of replacing the Gaussian assumption made by the working party with a more general stable distribution. It also explains how the appropriate stable distribution can be fitted.

scholarly journals An Universal, Simple, Circular Statistics-Based Estimator of α for Symmetric Stable Family

2019 ◽  
Vol 12 (4) ◽  
pp. 171
Author(s):  
Ashis SenGupta ◽  
Moumita Roy
Keyword(s):  
Entire Range ◽  
Goodness Of Fit ◽  
Stable Distribution ◽  
Real Life ◽  
Circular Statistics ◽  
Directional Statistics ◽  
Symmetric Stable Distribution ◽  
Stable Family ◽  
Family Of Distributions ◽  
Better Than

The aim of this article is to obtain a simple and efficient estimator of the index parameter of symmetric stable distribution that holds universally, i.e., over the entire range of the parameter. We appeal to directional statistics on the classical result on wrapping of a distribution in obtaining the wrapped stable family of distributions. The performance of the estimator obtained is better than the existing estimators in the literature in terms of both consistency and efficiency. The estimator is applied to model some real life financial datasets. A mixture of normal and Cauchy distributions is compared with the stable family of distributions when the estimate of the parameter α lies between 1 and 2. A similar approach can be adopted when α (or its estimate) belongs to (0.5,1). In this case, one may compare with a mixture of Laplace and Cauchy distributions. A new measure of goodness of fit is proposed for the above family of distributions.

A Stochastic Investment Model for Actuarial Use

1984 ◽  
Vol 39 ◽  
pp. 341-403 ◽  
Author(s):  
A. D. Wilkie
Keyword(s):  
Pension Fund ◽  
Working Party ◽  
Investment Model ◽  
Financial Contracts

1.1. The purpose of this paper is to present to the actuarial profession a stochastic investment model which can be used for simulations of “possible futures” extending for many years ahead. The ideas were first developed for the Maturity Guarantees Working Party (MGWP) whose report was published in 1980. The ideas were further developed in my own paper “Indexing Long Term Financial Contracts” (1981). However, these two papers restricted themselves to a consideration of ordinary shares and of inflation respectively, whereas in this paper I shall present what seems to me to be the minimum model that might be used to describe the total investments of a life office or pension fund.

A study on image denoising in contourlet domain using the alpha-stable family of distributions

2016 ◽  
Vol 128 ◽  
pp. 459-473 ◽  
Author(s):  
H. Sadreazami ◽  
M. Omair Ahmad ◽  
M.N.S. Swamy
Keyword(s):  
Image Denoising ◽  
Stable Family ◽  
Family Of Distributions

Report on the Wilkie stochastic investment model

1992 ◽  
Vol 119 (2) ◽  
pp. 173-228 ◽  
Author(s):  
T. J. Geoghegan ◽  
R. S. Clarkson ◽  
K. S. Feldman ◽  
S. J. Green ◽  
A. Kitts ◽  
...  
Keyword(s):  
Alternative Model ◽  
Working Party ◽  
Pension Funds ◽  
Investment Model ◽  
Arch Models ◽  
Future Developments ◽  
Life Assurance ◽  
Specific Alternative ◽  
Set Up ◽  
Investment Models

AbstractA FIMAG Working Party was set up in 1989 to consider the stochastic investment model proposed by A. D. Wilkie, which had been used by a number of actuaries for various purposes, but had not itself been discussed at the Institute. This is the Report of that Working Party. First, the Wilkie model is described. Then the model is reviewed, and alternative types of model are discussed. Possible applications of the model are considered, and the important question of ‘actuarial judgement’ is introduced. Finally the Report looks at possible future developments. In appendices, Clarkson describes a specific alternative model for inflation, and Wilkie describes some experiments with ARCH models. In further appendices possible applications of stochastic investment models to pension funds, to life assurance and to investment management are discussed.

scholarly journals A direct approach to the stable distributions

2016 ◽  
Vol 48 (A) ◽  
pp. 261-282 ◽  
Author(s):  
E. J. G. Pitman ◽  
Jim Pitman
Keyword(s):  
Functional Equation ◽  
Characteristic Function ◽  
Integral Representation ◽  
Explicit Form ◽  
Regular Variation ◽  
Stable Distribution ◽  
Stable Distributions ◽  
Direct Approach ◽  
Infinitely Divisible Distributions ◽  
Infinitely Divisible

AbstractThe explicit form for the characteristic function of a stable distribution on the line is derived analytically by solving the associated functional equation and applying the theory of regular variation, without appeal to the general Lévy‒Khintchine integral representation of infinitely divisible distributions.

scholarly journals Linear and Non-Linear Regression Models Assuming a Stable Distribution

2016 ◽  
Vol 39 (1) ◽  
pp. 109-128 ◽  
Author(s):  
Jorge A. Achcar ◽  
Sílvia R. C. Lopes
Keyword(s):  
Probability Density Function ◽  
Linear Regression ◽  
Posterior Distribution ◽  
Regression Models ◽  
Stable Distribution ◽  
Random Variable ◽  
Stable Distributions ◽  
Linear Regression Models ◽  
Non Linear ◽  
Computational Aspects

<p>In this paper, we present some computational aspects for a Bayesian analysis involving stable distributions. It is well known that, in general, there is no closed form for the probability density function of a stable distribution. However, the use of a latent or auxiliary random variable facilitates obtaining any posterior distribution when related to stable distributions. To show the usefulness of the computational aspects, the methodology is applied to linear and non-linear regression models. Posterior summaries of interest are obtained using the OpenBUGS software.</p>

A functional equation and its application to the characterization of the Weibull and stable distributions

1976 ◽  
Vol 13 (2) ◽  
pp. 385-391 ◽  
Author(s):  
Y. H. Wang
Keyword(s):  
Functional Equation ◽  
Weibull Distribution ◽  
Exponential Distribution ◽  
Stable Distribution ◽  
Stable Distributions ◽  
Cauchy Functional Equation ◽  
Linear Statistics

The Cauchy functional equation Φ(x + y) = Φ(x) + Φ(y) is generalized to the form , assuming Φ is left- or right- continuous. This result is used to obtain (1) a characterization of the Weibull distribution, in the spirit of the memoryless property of the exponential distribution, by , for all x, y ≧ 0;(2) a characterization of the symmetric α-stable distribution by the equidistribution of linear statistics.

A functional equation and its application to the characterization of the Weibull and stable distributions

1976 ◽  
Vol 13 (02) ◽  
pp. 385-391
Author(s):  
Y. H. Wang
Keyword(s):  
Functional Equation ◽  
Weibull Distribution ◽  
Exponential Distribution ◽  
Stable Distribution ◽  
Stable Distributions ◽  
Cauchy Functional Equation ◽  
Linear Statistics

The Cauchy functional equation Φ(x+y) = Φ(x) + Φ(y) is generalized to the form, assuming Φ is left- or right- continuous. This result is used to obtain (1) a characterization of the Weibull distribution, in the spirit of the memoryless property of the exponential distribution, by, for allx,y≧ 0;(2) a characterization of the symmetricα-stable distribution by the equidistribution of linear statistics.

scholarly journals Goodness-of-fit test for $$\alpha$$-stable distribution based on the quantile conditional variance statistics

2021 ◽  
Author(s):  
Marcin Pitera ◽  
Aleksei Chechkin ◽  
Agnieszka Wyłomańska
Keyword(s):  
Goodness Of Fit ◽  
Stable Distribution ◽  
Heavy Tails ◽  
Stable Distributions ◽  
Symmetric Case ◽  
Goodness Of Fit Test ◽  
Testing Procedures ◽  
Alpha Stable Distribution ◽  
Goodness Of Fit Tests ◽  
Distributional Properties

AbstractThe class of $$\alpha$$ α -stable distributions is ubiquitous in many areas including signal processing, finance, biology, physics, and condition monitoring. In particular, it allows efficient noise modeling and incorporates distributional properties such as asymmetry and heavy-tails. Despite the popularity of this modeling choice, most statistical goodness-of-fit tests designed for $$\alpha$$ α -stable distributions are based on a generic distance measurement methods. To be efficient, those methods require large sample sizes and often do not efficiently discriminate distributions when the corresponding $$\alpha$$ α -stable parameters are close to each other. In this paper, we propose a novel goodness-of-fit method based on quantile (trimmed) conditional variances that is designed to overcome these deficiencies and outperforms many benchmark testing procedures. The effectiveness of the proposed approach is illustrated using extensive simulation study with focus set on the symmetric case. For completeness, an empirical example linked to plasma physics is provided.

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