Extremes for coherent risk measures

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link: http://openaccess.city.ac.uk/16268/ Link to published version: http://dx.Abstract. Various concepts appeared in the existing literature to evaluate the risk exposure of a financial or insurance firm/subsidiary/line of business due to the occurrence of some extreme scenarios. Many of those concepts, such as Marginal Expected Shortfall or Tail Conditional Expectation, are simply some conditional expectations that evaluate the risk in adverse scenarios and are useful for signaling to a decision-maker the poor performance of its risk portfolio or to identify which sub-portfolio is likely to exhibit a massive downside risk. We investigate the latter risk under the assumption that it is measured via a coherent risk measure, which obviously generalizes the idea of only taking the expectation of the downside risk. Multiple examples are given and our numerical illustrations show how the asymptotic approximations can be used in the capital allocation exercise. We have concluded that the expectation of the downside risk does not fairly take into account the individual risk contribution when allocating the VaR-based regulatory capital, and thus, more conservative risk measurements are recommended. Finally, we have found that more conservative risk measurements do not improve the fairness of the cost of capital allocation when the uncertainty with parameter estimation is present, even at a very high level.

Systemic Risk: An Asymptotic Evaluation

“…, d}. Further, by Lemma 2.1 of Davis and Resnick (1996), we have Asimit and Li (2016) imply that, for every 0 < x ≤ 1,…”

“…For properties of the function h in (3.1), we refer the reader to Lemma 3.1 of Asimit and Li (2016). The following Proposition 3.1 gives some sufficient conditions to verify the asymptotic independence and asymptotic dependence between X and Y that satisfy Assumption 3.1 within the scope of regular variation and rapid variation.…”

“…We next show an example concerning the rapid variation case, in which the dependence structure is motivated by Mitra and Resnick (2009) (see also Asimit et al, 2011, Hashorva and Li, 2015, and Asimit and Li, 2016.…”

Systemic Risk: An Asymptotic Evaluation

“…1. This example is a special case of Example 4.3 of Asimit and Li (2016), by which we know that (4.16) also holds and X k ; S d satis…es Assumption 3.1 with…”

Investment Environment Problems Analysis and Evaluation: An Ex Post Empirical Analysis and Performance Implications

“…The evolution of risk management is induced by financial crises (Adrian, 2017). Special attention is given for measuring market risk (Brandtner, 2018;Ramponi, & Campi, 2017;Asimit & Li, 2016;Ouyang, 2009) and the necessity of volatility forecasting (Degiannakis, 2017;Zikes & Barunik, 2014), while recognizing investment and competitive environment (Prorokowski, 2016;Zukauskas, & Neverauskas, 2008). The practical implications are particularly significant in terms of analyzing the possibility of applying different VaR models, with ever-present challenges in determining an adequate level of reliability and an observation time interval.…”