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Pareto Chart00:52

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Relative risk (RR) is a statistical measure commonly used in epidemiology to compare the likelihood of a particular event occurring between two groups. This metric is important for evaluating the relationship between exposure to a specific risk factor and the probability of a particular outcome. It plays a crucial role in medical research, public health studies, and risk assessment. Relative risk quantifies how much more (or less) likely an event is to occur in an exposed group compared to an...
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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
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Risk Analysis via Generalized Pareto Distributions.

Y I He1, Liang Peng2, Dabao Zhang3

  • 1Amsterdam School of Economics, University of Amsterdam, Amsterdam 1001 NJ, The Netherlands.

Journal of Business & Economic Statistics : a Publication of the American Statistical Association
|June 27, 2022
PubMed
Summary

We compute financial risk using generalized Pareto distribution. Our new method improves threshold selection for accurate value-at-risk (VaR) estimation in finance and insurance.

Keywords:
ARMA-GARCH modelsGeneralized Pareto distributionRandom weighted bootstrapValue-at-riskWeighted empirical process

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Area of Science:

  • Quantitative Finance
  • Statistical Modeling
  • Risk Management

Background:

  • Value-at-Risk (VaR) is crucial for financial risk assessment.
  • Traditional methods often face challenges with threshold selection in extreme value analysis.
  • Existing studies on VaR estimation have limitations regarding threshold dependency.

Purpose of the Study:

  • To compute the value-at-risk (VaR) of financial losses.
  • To investigate the impact of threshold selection on maximum likelihood estimation for VaR.
  • To propose an improved method for interval estimation of VaR.

Main Methods:

  • Fitting a generalized Pareto distribution to data exceedances over a threshold.
  • Analyzing asymptotic variance for maximum likelihood estimation with varying thresholds.
  • Developing a random weighted bootstrap method for confidence interval estimation of VaR.

Main Results:

  • The asymptotic variance for maximum likelihood estimation is dependent on threshold choice for both independent and time-series data.
  • A novel random weighted bootstrap method provides reliable interval estimation for VaR.
  • Asymptotic results unify inference for both non-divergent and divergent thresholds.

Conclusions:

  • The proposed bootstrap method yields accurate confidence intervals for VaR.
  • The findings enhance VaR estimation accuracy in insurance and financial applications.
  • This research offers a more robust approach to quantifying financial risk.