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Risk aggregation with dependence uncertainty |
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| Institution: | 1. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L3G1, Canada;2. University of Waterloo, Canada;1. ING, Brussels, Belgium;2. Université Libre de Bruxelles, Brussels, Belgium;3. KU Leuven, Leuven, Belgium;4. Ghent University, Gent, Belgium;1. Amsterdam School of Economics, University of Amsterdam, The Netherlands;2. Faculty of Actuarial Science and Insurance, Cass Business School, City University London, United Kingdom;3. RiskLab, Department of Mathematics, ETH Zurich, Switzerland;1. Department of Financial Mathematics, Peking University, Beijing 100871, China;2. Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong;3. LMEQF, Department of Financial Mathematics, Peking University, Beijing 100871, China;1. University of Oslo, Norway;2. University of Barcelona, Spain;1. China Institute for Actuarial Science, Central University of Finance and Economics, China;2. KU Leuven, Leuven, Belgium;3. Faculty of Economics, Vrije Universiteit Brussel, Belgium |
| Abstract: | Risk aggregation with dependence uncertainty refers to the sum of individual risks with known marginal distributions and unspecified dependence structure. We introduce the admissible risk class to study risk aggregation with dependence uncertainty. The admissible risk class has some nice properties such as robustness, convexity, permutation invariance and affine invariance. We then derive a new convex ordering lower bound over this class and give a sufficient condition for this lower bound to be sharp in the case of identical marginal distributions. The results are used to identify extreme scenarios and calculate bounds on Value-at-Risk as well as on convex and coherent risk measures and other quantities of interest in finance and insurance. Numerical illustrations are provided for different settings and commonly-used distributions of risks. |
| Keywords: | Dependence structure Aggregate risk Admissible risk Convex risk measures TVaR Convex order Complete mixability VaR bounds |
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