Risk Aversion in Regulatory Capital Principles
SIAM Journal on Financial Mathematics, Forthcoming.
37 Pages Posted: 10 Sep 2015 Last revised: 26 Dec 2019
Date Written: October 1, 2018
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
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