Titlebook: Mathematical Risk Analysis; Dependence, Risk Bou Ludger Rüschendorf Book 2013 The Editor(s) (if applicable) and The Author(s), under exclus

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Dependence Orderings of Risk Vectors and PortfoliosThere are several dependence orderings ≺ for risk vectors ., . available which allow to infer conclusions of the type . ≺ . , i.e. . is stronger positive dependent than ., implies that . bears more risk than .. Of particular interest is the case where ., . have identical marginals, i.e. belong to the same Fréchet class.

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Law Invariant Convex Risk Measures on , and Optimal Mass TransportationAs explained before law invariant risk measures are of particular importance by the property that they allow empirical versions and statistical estimates.

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Optimal Contingent Claims and (Re)insurance ContractsWe consider in this chapter various problems on the construction of optimal contingent claims (respectively options) and of optimal contracts, in particular (re)insurance contracts. Some results of this type connected with optimal risk allocation have been given in Chapters 10 and 11.

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Optimal Portfolio Diversification w.r.t. Extreme RisksAfter an introduction to some basic notions of multivariate regular variation and extreme value theory we introduce the extremal risk index γ. which measures the extreme risk of the portfolio ξ.. and describe its dependence on the vector ξ of portfolio weights.

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Ludger RüschendorfUp-to-date treatment of the main concepts and techniques used in mathematical risk analysis.Clearly structured guide.Gives orientation and help to acquire a solid fundament for working in this area?.I

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