Inference for conditional value-at-risk of a predictive regression

He, Yi; Hou, Yanxi; Peng, Liang; Shen, Haipeng

doi:10.1214/19-aos1937

Cited by 5 publications

(2 citation statements)

References 41 publications

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“…Note that the main role of {w t } in our technical proofs is to bound the term w t y δ t−j for δ ≥ 1 by O(|y t−j | s ) for some s ∈ (0, 1). Following He et al (2020), we may consider…”

Section: Self-weighted Estimationmentioning

confidence: 99%

Quantile autoregressive conditional heteroscedasticity

Zhu

Tan

Yao

et al. 2023

Journal of the Royal Statistical Society Series B: Statistical Methodology

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This article proposes a novel conditional heteroscedastic time series model by applying the framework of quantile regression processes to the ARCH(∞) form of the GARCH model. This model can provide varying structures for conditional quantiles of the time series across different quantile levels, while including the commonly used GARCH model as a special case. The strict stationarity of the model is discussed. For robustness against heavy-tailed distributions, a self-weighted quantile regression (QR) estimator is proposed. While QR performs satisfactorily at intermediate quantile levels, its accuracy deteriorates at high quantile levels due to data scarcity. As a remedy, a self-weighted composite quantile regression estimator is further introduced and, based on an approximate GARCH model with a flexible Tukey-lambda distribution for the innovations, we can extrapolate the high quantile levels by borrowing information from intermediate ones. Asymptotic properties for the proposed estimators are established. Simulation experiments are carried out to access the finite sample performance of the proposed methods, and an empirical example is presented to illustrate the usefulness of the new model.

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Section: Self-weighted Estimationmentioning

confidence: 99%

Quantile autoregressive conditional heteroscedasticity

Zhu

Tan

Yao

et al. 2023

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…Using regression models, one obtains predictions for the losses based on a priori knowledge of the explanatory variables considered by the risk manager or actuary. Several papers developed and studied regression theory in the context of risks and risk measures (He et al, 2020;Keilbar & Wang, 2022;Gaglianone et al, 2011;Xiao et al, 2015;Barkai et al, 2021;Rennie & Srebro, 2005;Buccini et al, 2020;Ki Kang et al, 2020;Pitselis, 2020;Jeong & Valdez, 2020;Daouia et al, 2021). Unlike standard regression analysis, when dealing with risks one commonly wishes to focus on risk severity levels, which can be quantified by expected losses.…”

Section: Introductionmentioning

confidence: 99%

Optimizing insurance risk assessment: a regression model based on a risk-loaded approach

Landsman,

Shushi

2024

Ann. actuar. sci.

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Risk measurement and econometrics are the two pillars of actuarial science. Unlike econometrics, risk measurement allows taking into account decision-makers’ risk aversion when analyzing the risks. We propose a hybrid model that captures decision-makers’ regression-based approach to study risks, focusing on explanatory variables while paying attention to risk severity. Our model considers different loss functions that quantify the severity of the losses that are provided by the risk manager or the actuary. We present an explicit formula for the regression estimators for the proposed risk-based regression problem and study the proposed results. Finally, we provide a numerical study of the results using data from the insurance industry.

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