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This chapter introduces comonotonic additivity for risk measures, which states that the risk of a sum of comonotone variables equals the sum of their individual risks. Such risk measures are Choquet integrals with respect to a non-additive measure.
This chapter establishes dual representations of convex and coherent risk measures, demonstrating that they can be expressed as the supremum of affine functions or alternative scenarios.
Dynamic stochastic general equilibrium (DSGE) models have begun to dominate the field of macroeconomic theory and policy-making. These models describe the evolution of macroeconomic activity as a recursive sequence of outcomes based upon the optimal decision rules of rational households, firms and policy-makers. Whilst posing a micro-founded dynamic optimisation problem for agents under uncertainty, such models have been shown to be both analytically tractable and sufficiently rich for meaningful policy analysis in a wide class of macroeconomic problems, for example, monetary and fiscal policy, economic cycles and growth and capital flows. This volume collects specially commissioned papers from leading researchers, which pull together some of the key results in diverse areas. This book will promote research using optimising models and inform researchers, post-graduate students and economists in policy-oriented organisations of some of the key findings and policy implications.