Mathematical Risk Analysis Dependence, Risk Bounds, Optimal Allocations and Portfolios

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ISBN: 9783642335907
Physical Description: electronic
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XII, 408 p. 12 illus. online resource.
Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : 2013.

Subject:

Mathematics
Finance
Distribution (Probability theory)
Economics Statistics
Mathematics
Probability Theory and Stochastic Processes
Quantitative Finance
Actuarial Sciences
Applications of Mathematics
Operations Research, Management Science
Statistics for Business/Economics/Mathematical Finance/Insurance

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Table of Contents

	Preface.-Part I: Stochastic Dependence and Extremal Risk.-1 Copulas, Sklar's Theorem, and Distributional Transform
	2 FrÃ©chet Classes, Risk Bounds, and Duality Theory
	3 Convex Order, Excess of Loss, and Comonotonicity
	4 Bounds for the Distribution Function and Value at Risk of the Joint Portfolio
	5 Restrictions on the Dependence Structure
	6 Dependence Orderings of Risk Vectors and Portfolios
	Part II: Risk Measures and Worst Case Portfolios
	7 Risk Measures for Real Risks
	8 Risk Measures for Portfolio Vectors
	9 Law Invariant Convex Risk Measures on L_d p and Optimal Mass Transportation
	Part III: Optimal Risk Allocation
	10 Optimal Allocations and Pareto Equilibrium
	11 Characterization and Examples of Optimal Risk Allocations for Convex Risk Functionals
	12 Optimal Contingent Claims and (Re)Insurance Contracts
	Part IV: Optimal Portfolios and Extreme Risks
	13 Optimal Portfolio Diversification w.r.t. Extreme Risks
	14 Ordering of Multivariate Risk Models with Respect to Extreme Portfolio Losses
	References
	List of Symbols
	Index. â.

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