Risk Aversion in Regulatory Capital Principles

SIAM Journal on Financial Mathematics, Forthcoming.

37 Pages Posted: 10 Sep 2015 Last revised: 26 Dec 2019

See all articles by Tiantian Mao

Tiantian Mao

University of Science and Technology of China (USTC) - Department of Statistics and Finance

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: October 1, 2018

Abstract

We incorporate a notion of risk aversion favoring prudent decisions from financial institutions into regulatory capital calculation principles. In the context of Basel III, IV as well as Solvency II, regulatory capital calculation is carried out through the tools of monetary risk measures. The notion of risk aversion that we focus on has four equivalent formulations: through consistency with second-order stochastic dominance, or with conditional expectations, or with portfolio diversification, and finally through expected social impact. The class of monetary risk measures representing this notion of risk aversion is referred to as consistent risk measures. We characterize the class of consistent risk measures by establishing an Expected Shortfall-based representation, and as a by-product, we obtain new results on the representation of convex risk measures. We present several examples where consistent risk measures naturally appear. Using the obtained representation results, we study risk sharing and optimal investment problems and find several new analytical solutions.

Keywords: regulatory capital, risk aversion, risk sharing, stochastic dominance, diversification

Suggested Citation

Mao, Tiantian and Wang, Ruodu, Risk Aversion in Regulatory Capital Principles (October 1, 2018). SIAM Journal on Financial Mathematics, Forthcoming., Available at SSRN: https://ssrn.com/abstract=2658669 or http://dx.doi.org/10.2139/ssrn.2658669

Tiantian Mao

University of Science and Technology of China (USTC) - Department of Statistics and Finance ( email )

96, Jinzhai Road
Hefei, Anhui 230026
China

Ruodu Wang (Contact Author)

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

Waterloo, Ontario N2L 3G1
Canada

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