Author(s)

Martin M. Kithinji^1*, Peter N. Mwita², Ananda O. Kube³

¹Department of Mathematics, Institute for Basic Sciences, Technology and Innovation, Pan African University, Nairobi, Kenya.
²Department of Mathematics, Machakos University, Machakos, Kenya.
³Department of Statistics and Actuarial Sciences, Kenyatta University, Nairobi, Kenya.

In this paper, we present an estimator that improves the well-calibrated coherent risk measure: expected shortfall by restructuring its functional form to incorporate dynamic weights on extreme conditional quantiles used in its definition. Adjusted Extreme Quantile Autoregression will is used in estimating intermediary location measures. Consistency and coherence of the estimator are also proved. The resulting estimator was found to be less conservative compared to the expected shortfall.

Exreme Quantile Autoregression, Expected Shortfall, Value at Risk, Coherence, Risk Measurement

Kithinji, M. , Mwita, P. and Kube, A. (2021) Estimation of Conditional Weighted Expected Shortfall under Adjusted Extreme Quantile Autoregression. Journal of Mathematical Finance, 11, 373-385. doi: 10.4236/jmf.2021.113021.