Project

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Extremal Behaviour of Random Scaling Models

English title Extremal Behaviour of Random Scaling Models
Applicant Hashorva Enkelejd
Number 134785
Funding scheme Project funding (Div. I-III)
Research institution HEC - Ecole des Hautes Etudes Commerciales Université de Lausanne
Institution of higher education University of Lausanne - LA
Main discipline Mathematics
Start/End 01.06.2011 - 31.05.2014
Approved amount 164'424.00
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Keywords (20)

random scaling; Dirichlet process; Gaussian process; fractional Laplace motion; Brown-Resnick process; elliptical process; max-domain of attractions; tail asymptotics; Weibullian tails; second order extreme value conditions; max-stable distributions; conditional limiting theorems; Kotz approximation; asymptotic independence; Hüsler-Reiss triangular arrays; Dirichlet distributions; elliptical distributions; ruin probability; missing values; maxima of Gaussian processes

Lay Summary (English)

Lead
Lay summary
This project aims to investigate the extremal behaviour of some important discrete and continuous random scaling models. Typically, random scaling models the presence of deflators or inflators in finance and insurance, the impact of measurement errors, missing values or latent shocks in statistics, or the influence  of random time deformations for certain stochastic processes.  The tractability of random scaling models and their natural emergence explains their wide applicability in statistics, finance and insurance, stochastic geometry, stochastic analysis, or physics. By relying on new asymptotic techniques  and recent progress of extreme value theory this project investigates the extremal properties of different random scaling models envisaging  novel applications and theoretical results related to  ruin theory, risk management, and extreme value theory. Further, with emphasis on theoretical results, this projects explores the effect of random scaling on the extremal behaviour of certain stochastic processes.
Direct link to Lay Summary Last update: 21.02.2013

Responsible applicant and co-applicants

Employees

Publications

Publication
Limit laws for maxima of contracted stationary Gaussian sequences
Hashorva Enkelejd, Weng Zhichao (2015), Limit laws for maxima of contracted stationary Gaussian sequences, in Communications in Statistics - Theory and Methods, 44, 4641-4641.
Maxima of independent, non-identically distributed Gaussian vectors
Engelke Sebastian, Kabluchko Zakhar, Schlather Martin (2015), Maxima of independent, non-identically distributed Gaussian vectors, in Bernoulli, 21(1), 38-61.
ASYMPTOTICS FOR A DISCRETE-TIME RISK MODEL WITH THE EMPHASIS ON FINANCIAL RISK
Hashorva Enkelejd, Li Jinzhu (2014), ASYMPTOTICS FOR A DISCRETE-TIME RISK MODEL WITH THE EMPHASIS ON FINANCIAL RISK, in PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES, 28(4), 573-588.
Second-order tail asymptotis of deflated risks
Hashorva E., Ling C., Peng Z. (2014), Second-order tail asymptotis of deflated risks, in Insurance: Mathematics & Economics, 56, 88-101.
Tail asymptotic of Weibull-type risks.
Hashorva Enkelejd, Weng Zichao (2014), Tail asymptotic of Weibull-type risks., in Statistics, 48(5), 1155-1165.
Dependence modelling in multivariate claims run-off triangles
Merz M., Wüthrich M.V., Hashorva E. (2013), Dependence modelling in multivariate claims run-off triangles, in Annals of Actuarial Science, 7(1), 3-25.
Extremes and products of multivariate AC-product risks
Yang Y., Hashorva E. (2013), Extremes and products of multivariate AC-product risks, in Insurance: Mathematics and Economics, 52(2), 312-319.
Large deviations for proportions of observations which fall in random sets determined by order statistics
Hashorva E, Macci C, Pacchiarotti B (2013), Large deviations for proportions of observations which fall in random sets determined by order statistics, in Methodology and Computing in Applied Probability, 15(4), 875-896.
Limit laws for extremes of dependent stationary Gaussian arrays
Hashorva Enkelejd, Weng Zhichao (2013), Limit laws for extremes of dependent stationary Gaussian arrays, in Statistics and Probability, Letters, 83, 320-330.
Minima and maxima of elliptical triangular arrays and spherical processes
Hashorva Enkelejd (2013), Minima and maxima of elliptical triangular arrays and spherical processes, in Bernoulli, 19(3), 886-904.
Scale mixtures of Kotz–Dirichlet distributions
Balakrishnan N, Hashorva E (2013), Scale mixtures of Kotz–Dirichlet distributions, in J. Multivariate Analysis, 113, 48-58.
Gaussian approximation of conditional elliptical copulas
Hashorva E, Jaworski P (2012), Gaussian approximation of conditional elliptical copulas, in Journal Multivariate Analysis, 111, 397-407.
Joint limit distributions of exceedances point processes and partial sums of gaussian vector sequence
Peng Z, Tong J.J., Weng Z. (2012), Joint limit distributions of exceedances point processes and partial sums of gaussian vector sequence, in Acta Mathematica Sinica, English Series, 28(8), 1647-1662.
On the infinite sums of deflated Gaussian products
Hashorva Enkelejd, Ji Lanpeng, Tan Zhongquan (2012), On the infinite sums of deflated Gaussian products, in Electron. Commun. Probab. , (17), 1-8.
Archimedean copulas in finite and infinite dimensions-with application to ruin problems
Constantinescu C, Hashorva E, Ji L (2011), Archimedean copulas in finite and infinite dimensions-with application to ruin problems, in Insurance: Mathematics and Economics, 49(3), 487-495.

Collaboration

Group / person Country
Types of collaboration
University Tor Vergata, Rome Italy (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
ETH Zurich, Risk Lab Switzerland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
University of Wroclaw Poland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
University of Nankai China (Asia)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
- Exchange of personnel
University of Warsaw Poland (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Southwest University China (Asia)
- in-depth/constructive exchanges on approaches, methods or results
- Publication

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
Stochastic Networks And Risk Analysis IV Talk given at a conference Extremes of Chi-processes 26.05.2014 Bedlewo, Poland Hashorva Enkelejd;
56e Journée de séminaires actuariels Individual talk Estimation of Brown-Resnick processes based on single extreme events 21.03.2014 Lyon, France Engelke Sebastian;
RARE Seminar, University of Liverpool Individual talk Asymptotic Expansions of Ruin Probability for the Time-Changed fBM Risk Process 23.01.2014 Liverpool, Great Britain and Northern Ireland Hashorva Enkelejd;
55e Journée de séminaires actuariels Talk given at a conference Random Scaling and Shifting of Dependent Risks 08.11.2013 Lausanne, Switzerland Hashorva Enkelejd;
Extreme Value Conference EVA 2013, Fudan University, Shanghai Individual talk A scaled normal comparison inequality and its application 10.07.2013 Shanghai, China, China Weng Zhichao;
17th International Congress on Insurance Mathematics and Economics Talk given at a conference Tail Asymptotic of Weibull-Type Risks 01.07.2013 Copenhagen, Denmark Weng Zhichao;
ESD Seminars Individual talk Estimation of Brown-Resnick Processes Based on Single Extreme Events 26.06.2013 Singapore University of Technology and Design, Singapore Engelke Sebastian;
Perspectives on Actuarial Risks in Talks of Young Researchers Individual talk Brown-Resnick Processes based on Levy Processes 28.01.2013 Monte Verita, Ascona, Switzerland, Switzerland Engelke Sebastian;
International Conference on Actuarial Science and Risk Management, Xiamen University, China Individual talk On Random Shifting and Scaling In Actuarial Applications 24.06.2012 China, China Weng Zhichao;
IWAP 2012 - International Workshop on Applied Probability Individual talk Finite-time Ruin Probability of Aggregated Gaussian Processes With Trend 11.06.2012 Jerusalem, Israel Hashorva Enkelejd;
FASI Seminar, CASS Business School, London Individual talk Extremal Behaviour of Aggregated Dependent Risks 07.03.2012 London, Great Britain and Northern Ireland Hashorva Enkelejd;
International Conference on Advances in Probability and Statistics - Theory and Applications: Individual talk On Person-Kotz Dirichlet Random Vectors 28.12.2011 Chinese University of Hong Kong, Hong Kong, PR China, Hongkong Hashorva Enkelejd;
Stochastic Seminar, University of Umea Talk given at a conference Limits Theorems for Multivariate Maxima & Minima of Triangular Arrays 28.09.2011 Umea, Sweden, Sweden Hashorva Enkelejd;
7th Conference on Extreme Value Analysis, Probabilistic and Statistical Models and their Applications Poster Rates of convergence of extremes for mixed exponential distributions 27.06.2011 Lyon, France, France Weng Zhichao;
15th International Congress on Insurance:Mathematics and Economics Individual talk Archimedean copula in (in)nite dimensions some applications to ruin problems 14.06.2011 Trieste, Italy, Italy Hashorva Enkelejd;


Knowledge transfer events

Active participation

Title Type of contribution Date Place Persons involved
AGLA Annual Meeting 2012 Talk 26.04.2012 Lausanne, Switzerland Hashorva Enkelejd;
Arbeitsgruppentagung SAV ASTIN, Bern Talk 02.09.2011 Bern, Switzerland Hashorva Enkelejd;


Abstract

This project aims to investigate the extremal behaviour of some important discrete and continuous random scaling models. Two canonical instances of random elements defined by random scaling are the Gaussian and the Dirichlet processes. Typically, random scaling models the presence of deflators or inflators in finance and insurance, the impact of measurement errors, missing values or latent shocks in statistics, or the influence of random time deformations for certain stochastic processes. The tractability of random scaling models and their natural emergence explains their wide applicability in statistics, finance and insurance, stochastic geometry, stochastic analysis, or physics.Recent research has shown that certain conditional limit theorems, tail approximation of Dirichlet distributions, asymptotic independence of polar random vectors, the extremal behaviour of specific aggregated risks, or the asymptotics of the maxima of elliptical processes are direct consequences of the underlying scaling phenomena.On the statistical side, the study of random scaling models paves new ways for estimating rare events influenced by large scaling effects, as well as for dealing with diverse patterns of missing observations.By relying on new asymptotic techniques and recent progress of extreme value theory this projects investigates the extremal properties of different random scaling models envisaging novel applications and theoretical results related to ruin theory, risk management, and extreme value theory.Another direction of the project with emphasis on theoretical results explores the effect of random scaling on the maxima and minima of elliptical and related stochastic processes, and studies the asymptotics of the maximum of those processes over random time intervals.
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