Worst-Case Range Value-at-Risk with Partial Information

35 Pages Posted: 21 Feb 2017

See all articles by Lujun Li

Lujun Li

Peking University

Hui Shao

National University of Singapore (NUS) - Risk Management Institute

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Jingping Yang

Peking University - School of Mathematical Sciences

Date Written: February 19, 2017

Abstract

In this paper, we study the worst-case scenarios of a general class of risk measures, the Range Value-at-Risk (RVaR), in single and aggregate risk models with given mean and variance, as well as symmetry and/or unimodality of each risk. For different types of partial information settings, sharp bounds for RVaR are obtained for single and aggregate risk models, together with the corresponding worst-case scenarios of marginal risks and the corresponding copula functions (dependence structure) among them. Different from the existing literature, the sharp bounds under different partial information settings in this paper are obtained via a unified method combining convex order and the recently developed notion of joint mixability. As particular cases, bounds for Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) are derived directly. Numerical examples are also provided to illustrate our results.

Keywords: model uncertainty, risk aggregation, Range Value-at-Risk, Value-at-Risk, Tail Value-at-Risk, convex order

Suggested Citation

Li, Lujun and Shao, Hui and Wang, Ruodu and Yang, Jingping, Worst-Case Range Value-at-Risk with Partial Information (February 19, 2017). Available at SSRN: https://ssrn.com/abstract=2920334 or http://dx.doi.org/10.2139/ssrn.2920334

Lujun Li

Peking University ( email )

No. 38 Xueyuan Road
Haidian District
Beijing, Beijing 100871
China

Hui Shao

National University of Singapore (NUS) - Risk Management Institute ( email )

21 Heng Mui Keng Terrace
Level 4
Singapore, 119613
Singapore

Ruodu Wang (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Jingping Yang

Peking University - School of Mathematical Sciences ( email )

Peking
China

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