This book gives an introduction to basic concepts and methods in mathematical risk
analysis, in particular to those parts of risk theory which are of particular relevance in finance …

Over the last decade, it has been shown that the concept of comonotonicity is a helpful tool
for solving several research and practical problems in the domain of finance and insurance …

We address the problem of risk sharing among agents using a two-parameter class of
quantile-based risk measures, the so-called range-value-at-risk (RVaR), as their …

In this paper we provide a complete solution to the existence and characterization problem
of optimal capital and risk allocations for not necessarily monotone, law-invariant convex risk …

The optimal insurance problem represents a fast growing topic that explains the most
efficient contract that an insurance player may get. The classical problem investigates the …

Using a standard reduction argument based on conditional expectations, this paper argues
that risk sharing is always beneficial (with respect to convex order or second degree …

We present and compare two different approaches to conditional risk measures. One
approach draws from convex analysis in vector spaces and presents risk measures as …

This paper studies efficient risk-sharing rules for the concave dominance order. For a
univariate risk, it follows from a comonotone dominance principle, due to Landsberger and …

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Two by-now folkloric results in the theory of risk sharing are that (i) any feasible allocation is
convex-order-dominated by a comonotonic allocation; and (ii) an allocation is Pareto optimal …