RISK MEASURES: RATIONALITY AND DIVERSIFICATION

Simone Cerreia‐Vioglio · Fabio Maccheroni · Massimo Marinacci B · Luigi Montrucchio

120 citations0/0 files storedMathematical Finance

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Risk and Portfolio Optimization Stochastic processes and financial applications Probability and Risk Models

Abstract

When there is uncertainty about interest rates (typically due to either illiquidity or defaultability of zero coupon bonds) the cash-additivity assumption on risk measures becomes problematic. When this assumption is weakened, to cash-subadditivity for example, the equivalence between convexity and the diversification principle no longer holds. In fact, this principle only implies (and it is implied by) quasiconvexity. For this reason, in this paper quasiconvex risk measures are studied. We provide a dual characterization of quasiconvex cash-subadditive risk measures and we establish necessary and sufficient conditions for their law invariance. As a byproduct, we obtain an alternative characterization of the actuarial mean value premium principle.

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References

1999Coherent Measures of Risk 1961Risk, Ambiguity, and the Savage Axioms 1989Maxmin expected utility with non-unique prior 1972Capital Market Equilibrium with Restricted Borrowing 1959Theory of Value 2004Subjective probability and expected utility without additivity 1989Subjective Probability and Expected Utility without Additivity 2002Convex measures of risk and trading constraints

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